As far as I know the GPL does not allow trial periods and asking for money later on, but feel free to correct me. That's why elementary cannot do such a thing.
GPL just requires source to be available to anyone who receives the binary. It has to be available on request. You can ask them to pay for the cost of postage to ship it to them.
Hell, you can ask them to pay anything, like RedHat does, regardless of costs. It's perfectly legal and GPL-compliant. You just have to provide sources.
No, I didn't mean a trial version. I just suggested they should ask for a donation once people actually had the chance to find out if they'd consider donating worth it.
The GPL and payment are orthogonal. They could GPL a piece of software that stops working after 30 days if you don't pay. You decide if to compile out the code that checks for the payment (and possibly distribute your version) or pay them those money.
If Elementary wants to alter some program to add a time bomb, the GPL cannot stop them. The GPL only ensures that the user can take the time bomb out (either by themselves or by following instructions on the internet, or by hiring somebody to do it).
No. Gpl has no such thing. But you'll have to provide the source code with your software, so I'll just modify the source to give myself infinite trial.
It'll work, it just won't get quite as many conversions as it might otherwise. The same principle applies to closed-source software, after all: you have to provide the binary, so I'll just modify the binary to give myself an infinite trial. This is entirely doable, but enough people still pay to make it a viable business in many cases.
The number of people that would bother to do that is relatively small. If it's a good product, and reasonably priced, people would much rather just pay to have it. (See music streaming.)