I am very glad you asked these questions, because as GM, I have a very clear picture of the setting and this there is a breakdown in relay this information efficiently all the time. You're right to ask, the OP was probably too sparse of mech details. I'll post my exact thoughts, but it is all up for debate/discussion. 
Q: What's the basic size of current era mechs? Does it vary from faction to faction? Has artillery evolved along side them? How so? Do cannons crab around on legs or are there just blockier mechs with big guns?
A: The 'era' I keep saying I'm pushing is real-robotish. With a bit more lenience for sci fi tech given it's 60+ in the future: rail based rifles, basic energy weapons, etc. Though I realise cyberwarfare would be a pretty big aspect also. Sizes would for example from 5 meters tall up to like 20, nothing going near 50, fifty meters is very tall. Tech levels will obviously vary here and there, but basic design goals would be similar. A good comparison is aircraft arms races and developments. Yes crab tanks exist, as seen in my CS. They 'running tanks' were staples of the European forces.
Q: You mentioned that mechs won't be hoofing it cross country. Do they lie down on flatbeds/stow inside transport planes after every engagement or do most designs incorporate a wheeled drive? If so please describe it.
A: Well maybe the mechs should be running around? I just didn't expect them to stroll from France to Germany say? Within deployment zones they'd move 'on foot' like infantry but for long range deployment, specialized transports would be used; land, air and sea. The wheeled drive system is something that's maybe used in conjunction with 'walking' maneuvers.
Q: Your CS mentioned how the Federation's 4 gen Dragoons make use of neural assisted targeting. Is battle fatigue a major concern? Do several pilots crew the same suit and operate in shifts? Would damaging/overloading/overstimulating this system over-stress the pilot? Is there a secondary targeting system in case of malfunction?
A: In my CS it notes comas were caused in three specifically trained pilots after prolonged use of entirely neural systems. So yes, battle fatigue is an element that exists. Of course you'd expect fairly rigorous training among pilots, preventative measures and the whole sci-fi lends itself to pilots themselves being enhanced beyond regular operational limits. Yes there could be potential cause of stress in pilots due to malfunctioning neural systems. I'd assume our engineers know what they're doing and have redundancy built in, including manual aiming and firing mechanisms.
Q:*What powers most mechs? If it's not diesel why does everyone need oil so badly? Solely for civilian and manufacturing needs? If so why haven't they begun to shift to secondary energy sources?
A: Good question, I hadn't put huge thought into the setting's Applied Phlebtonium, and had just used oil as its a well known substance/energy source. Diesel mechs may be a bit too grungy for the feel we're going for. I'm open to suggestions on this one. I'm much more used to writing in hard space opera settings, so these down to earth sci fi techs aren't my forte! Some possible ideas include; a new refining method for the oil, compact nuclear reactors but they have obvious issues with mass production and inevitable destruction, and just coming up with some magic plot compound like most mech settings do.
Q:*Operation and maintenance times/costs for mechs please? Just a rough ballpark estimate would be great. How far could most mechs travel on their own/ how long could they maintain combat readiness without refuel/repairs? Are more modern/sophisticated mechs more vulnerable to this than older, out-dated models?
A: Ha! Going to answer this based on my actual job as an aircraft quality assurance engineer! Assuming the mechs are of an equal tech level in their own setting, and the average technician is as skilled as those working with me, a minor maintenance could take place in hours, large repairs and replacements in a day or two and complete overhauls would be a week or so. Homeland Empire maintenance stations might be able to do thirty overhauls a day though, and underground resistance garages might struggle to weld panels back on. It's a bit relative this one. We can assume older mechs are more prone to total failure, but mechs with more complex systems are more prone to regular minor issues. Bare in mind though that again, the term 'complex' is a very subjective.
Q:*How vulnerable are mechs to air-to-ground based bombardment? As in helicopters/planes. One would assume very--but then it raises the question of anti-air mechs. Are their any flight-capable mechs?
A: You'd assume it's a two way fiasco, with many basic mech models being prone to bombardment, but some advanced models being agile enough to attempt to avoid it. There's inevitably going to be AA based mechs, flaks and missiles and such.
Q: What's the basic size of current era mechs? Does it vary from faction to faction? Has artillery evolved along side them? How so? Do cannons crab around on legs or are there just blockier mechs with big guns?
A: The 'era' I keep saying I'm pushing is real-robotish. With a bit more lenience for sci fi tech given it's 60+ in the future: rail based rifles, basic energy weapons, etc. Though I realise cyberwarfare would be a pretty big aspect also. Sizes would for example from 5 meters tall up to like 20, nothing going near 50, fifty meters is very tall. Tech levels will obviously vary here and there, but basic design goals would be similar. A good comparison is aircraft arms races and developments. Yes crab tanks exist, as seen in my CS. They 'running tanks' were staples of the European forces.
Q: You mentioned that mechs won't be hoofing it cross country. Do they lie down on flatbeds/stow inside transport planes after every engagement or do most designs incorporate a wheeled drive? If so please describe it.
A: Well maybe the mechs should be running around? I just didn't expect them to stroll from France to Germany say? Within deployment zones they'd move 'on foot' like infantry but for long range deployment, specialized transports would be used; land, air and sea. The wheeled drive system is something that's maybe used in conjunction with 'walking' maneuvers.
Q: Your CS mentioned how the Federation's 4 gen Dragoons make use of neural assisted targeting. Is battle fatigue a major concern? Do several pilots crew the same suit and operate in shifts? Would damaging/overloading/overstimulating this system over-stress the pilot? Is there a secondary targeting system in case of malfunction?
A: In my CS it notes comas were caused in three specifically trained pilots after prolonged use of entirely neural systems. So yes, battle fatigue is an element that exists. Of course you'd expect fairly rigorous training among pilots, preventative measures and the whole sci-fi lends itself to pilots themselves being enhanced beyond regular operational limits. Yes there could be potential cause of stress in pilots due to malfunctioning neural systems. I'd assume our engineers know what they're doing and have redundancy built in, including manual aiming and firing mechanisms.
Q:*What powers most mechs? If it's not diesel why does everyone need oil so badly? Solely for civilian and manufacturing needs? If so why haven't they begun to shift to secondary energy sources?
A: Good question, I hadn't put huge thought into the setting's Applied Phlebtonium, and had just used oil as its a well known substance/energy source. Diesel mechs may be a bit too grungy for the feel we're going for. I'm open to suggestions on this one. I'm much more used to writing in hard space opera settings, so these down to earth sci fi techs aren't my forte! Some possible ideas include; a new refining method for the oil, compact nuclear reactors but they have obvious issues with mass production and inevitable destruction, and just coming up with some magic plot compound like most mech settings do.
Q:*Operation and maintenance times/costs for mechs please? Just a rough ballpark estimate would be great. How far could most mechs travel on their own/ how long could they maintain combat readiness without refuel/repairs? Are more modern/sophisticated mechs more vulnerable to this than older, out-dated models?
A: Ha! Going to answer this based on my actual job as an aircraft quality assurance engineer! Assuming the mechs are of an equal tech level in their own setting, and the average technician is as skilled as those working with me, a minor maintenance could take place in hours, large repairs and replacements in a day or two and complete overhauls would be a week or so. Homeland Empire maintenance stations might be able to do thirty overhauls a day though, and underground resistance garages might struggle to weld panels back on. It's a bit relative this one. We can assume older mechs are more prone to total failure, but mechs with more complex systems are more prone to regular minor issues. Bare in mind though that again, the term 'complex' is a very subjective.
Q:*How vulnerable are mechs to air-to-ground based bombardment? As in helicopters/planes. One would assume very--but then it raises the question of anti-air mechs. Are their any flight-capable mechs?
A: You'd assume it's a two way fiasco, with many basic mech models being prone to bombardment, but some advanced models being agile enough to attempt to avoid it. There's inevitably going to be AA based mechs, flaks and missiles and such.
Someone finally asked one of the obvious questions.
this guys got the numbers.
you answered with essentially what I would have said.