1. Both sides do get a benefit from a trade route but there is a difference. The one sending the freighter gets a variable benefit - the game will inform you of the range when the route is formed - which will increase over time, I believe. The side receiving the freighter gets a fixed income which I think is the base value of the route without the variable part. I don't know if that increases over time.
So, both sides benefit from trade but the one sending the freighter gains more.
2. The economy starbases can improve trade routes by installing trade modules (unlocked by the trade tech tree). Their benefit only applies when the little freighter is within range of the starbase. This puts you for a choice: do you build starbases around one planet that acts as the centre of your trading empire so they cover all routes at the base? Or do you build them at the end where the net result is higher but you probably won't have much use for the production modules? Obviously, you can just do both.
Just wanted to point out the choice you have.
3. The distance affects the maximum value of the trade route, not the base value. I'm not sure if and how population affects the value. I send my freighters from my homeworld but that's just me.
Hope this helped you a bit.