There are many places where, not only is the power company unwilling to pay, they are unwilling to take it for free.
1. I figure there's exceptions, thus the 'to my knowledge'. That being said, citation please.
2. You always need an inverter unless you're only using DC appliances.
3. Of course, when 'green energy' was only starting they didn't want you feeding back into the grid. The rules hadn't been set up for safety and stability yet. They have enough problems with people backfeeding onto the power lines and endangering workers with generators.
4. Grid usage fee - it's spreading, but most 'customer fees' are more for paying the meter readers and billing system*. Connection charges can vary widely.
Still, some seem to be wanting to avoid the issue entirely - things like charging $60/month specifically for a solar setup(in addition to other static charges), when many people(like me) actually use less than $60 worth of electricity** a month anyways.
Of course, you also run into that many places have used their utilities as a sort of welfare platform. See California's reverse pricing scheme - rather than making electricity cheaper in bulk, like in most goods, and as seen when sold to industrial customers, they make it more expensive the more you use.
So where social reformers have a fair bit of control over pricing, you can see power companies having pricing schemes that cost them money on low-use customers, which those that mount solar panels imitate.
*And by golly they have to have the most inefficient meter readers and gold-plated billing system ever if it costs $20/month just to send me a bill.
**My bill is usually around $100/month due to the surcharges.