I've noticed that you can get Solar from killing enemy heroes, collecting it on the map and killing enemy drones. Are there other methods apart from these? How much Solar do you get from these things?
there are several ways, but I find destroying droids to be the most effective. They are numerous, but easy to kill. Each droid gives 5 solar, if you destroy many of them, the benefit is significant.
Killing enemy Awesomenauts gives solar not only to you, but also to the whole team. The killer receives more, of course.
Solar tree and piggy bank can be of some use here as well. Piggy bank is cool if you need to boost yourself with some particular ability right in the beginning of the game, and solar tree is the saviour during long matches.
Some heroes (Raelynn and Winnie&Spike) have additional upgrades that boost Solar output upon something (for example, killing enemy player).
Destroying enemy turret yields solar (about 30-50, not sure), but there are often enemies which are waiting to gather it all. Unless it is you who delivers the final blow to the turret, of course.