1/ My M/C resources are maxed out at 999,999... so, how do you buy stuff from Zenith trader that costs upwards of millions?
When you buy from the Zenith Trader, you don't pay the entire cost upfront. Rather, you buy, I guess, the blueprints (for free) and then foot the bill while you're building it. So it's basically like paying off a mortgage loan.
2/ Did I understand correctly that I can collect knowledge without capturing a planet by just sending (heavily defended) research labs and try and keep them alive until I gather the 3,000 knowledge? Are they very vulnerable to Guardians and Posts? Can I sneak them in on a transport?
You can collect knowledge without capturing a planet "knowledge raiding" using a mark 3 science station. These can't move, however, so what you need to do is take a mobile builder (preferably in a transport) and probably unload the builder at the edge of the system to build it. You'll draw a lot of aggression, so it's probably best not to do this on a planet with an active AI eye, ion cannons, armor boosters etc, because you'll need a force defending the science lab of a considerable size to hold it for the entire time it takes to build and collect the knowledge. It's normally a lot easier to just take a system.
3/ Even with mark III scouts I really take a beating when I try to recon planets more than 4 hops away... and scout starships (Mk I) seem super weak. Am I missing something? I haven't tried yet to send them on a transport.
The AI probably has a lot of Tachyon guardians around the wormholes you're sending scouts through. If this is the case, it may be worth using raid starships or transports to destroy the tachyon guardians in the closest systems, which should give you a bit more range. Alternatively, you can put your scouts in a transport, which should last about 3 jumps, and then the scouts themselves should go a fair bit further. In general scouting has been rebalanced a lot so it's hard to tell how far you should be getting. It's possible you're up against a counterspy AI.
4/ Given my current position, I'm really tempted to catch my next planet 2 or 3 hops away where the fight is worth the cost (e.g. the next adv research station). But I guess that means that I will not have a supply line if I destroy the AI base there and set up my command station. How penalizing will that be? Very nervous about splitting my forces in two, specially if I need reinforcements.
You'll probably have to get used to planet hopping if you want to win your game, as the progress cost of keeping supply lines everywhere is extremely high. That said, you can still reinforce to locations that you don't have direct lines to, using gates (I forget what they're called exactly). I think they're in the construction tab, but basically you can build gates that will port all the forces produced from a certain type of facility, so anything made from a space dock will appear at one of these gates (they split randomly if you have more than one). Basically, build gates at your outlying planets, and one on your homeworld, and you can power them down and up to direct the flow of ships to various areas of your empire depending on your need. If you're at the ship cap, you can also scrap some ships if you need to quickly port them to a different part of the galaxy (by rebuilding to different gates).
5/ Related to the above, I'm really not clear as to the best sequential way to capture a planet with lots of exotic stuff on it... where should I concentrate my forces? Who should I take out first? Should I always take the command station last? A vast topic I know, but a couple of pointers is all I'm looking for. I often find myself compelled to take down the nasty posts for fear that with all their long range weaponry they will wipe me out.
The first thing I take out is generally the Ion cannons. Raid starships are good for this. Usually it's a good idea to clear out the guard posts and guardians before taking the command station, but if the planet is looking really tough to crack you can raid the command station, which will turn the entire planet aggressive. As long as you have strong defenses, this might be easier. In general, once ion cannons are down, take out sniper and mlrs/artillery guardposts and guardians, special forces guardposts, etc. You need to destroy all the guardposts (except wormhole ones) to take out an AI eye.
Hope that helps a bit.