Welcome to the forums! And glad you're enjoying the game, even if having a tough time. To your questions:
1) Well, energy reactors cost you a lot of metal and crystal, so usually that is it. If you want to see where you are spending a ton of metal, just open the stats screen (click on the scores box), and then look at the Expenses By Player tab there. That gives you the rundown on literally every metal/crystal expenditure in your empire. It might just be that you haven't captured enough metal to really support the sort of economy you want at present. I generally aim for a gross metal/crystal income of around 500 or so at least by mid-game. If you have not been already, you may want to build metal manufactories to convert your crystal excesses into metal.
2) That's really not that many ships on those planets, honestly. If you leave them for a while longer, they'll both wind up with around 4000ish of that level ships on there. Different planets around the galaxy have different marks, independent of the overall level. Have you played the intermediate tutorial for the game? That is talked about in there a bit (along with many other topics), and it's really something that is well worth your while if you skipped it. You'll probably want to use transports to get around those big planets.
3) Again, the intermediate tutorial teaches you several strategies for dealing with ion cannons. If you skip the intermediate tutorial, you're likely to be confused, as this game is sooo very different from most other strategy games. You'll either want to "flood" the ion cannon (ie, rush it and kill it with low level ships), or send in higher level ships, or send in ships to pop out of a transport and surprise attack it. Starships have many varied uses, depending on the starships line, ranging from increasing the power of the rest of your fleet, to taking out other starships, to going on long range raids themselves, to converting enemy ships to your own use, to shooting out the engines of massive numbers of enemy ships... and so on.
4) Lots of people love using the lightning warheads to clear wormholes on enemy planets that are high level (as you mentioned having trouble with in #3), but nukes are a weapon of last resort. If you need one you
really need one, usually, but they aren't to be used lightly for sure.
For strategy tips in general, please make sure you play the in-game tutorials. You won't be prepared for the game without them, for sure. And, you may want to have a look at the various strategies in the
official wiki, which breaks down a lot of specific topics in more depth (check out the offensive and defensive sections in particular, I'd suggest). There is also a strategy discussion subforum here, where a ton of people (newbies and experts alike) discuss various topics, and where you can ask further questions that might remain after the other venues are all exhausted. Also, some
video tutorials if you want. You may find the ones on general tactics to be of particular note, in that one.