Yes, you can use Synfig any way you like. It’s open source software under the GPL licence.
Yes you can. Output will go way over 1080. You can most certainly output 4K material (4096×3072). I would recommend outputting to png-sequences for use in an edit software.
You can link to external canvases and you can import image sequences (made from video). Not exactly sure how movie clip symbols work in flash, but I think it’s something like exporting an canvas in Synfig.
I have read that GNU GPL licences allow people to make derivative works. Does this mean people can make derivative copies of my animation made with synfig without asking me permission? I’m a bit confused.
Will I have full ownership of my work or will it be under GNU terms?
It is the software which is released under GPL 2 or above license. The license talks about the program and its modifications (source code). Any creation made with the software belongs to you and you can license it under whatever license you want. You can earn money with your work and protect it against illegal copies (if it is what you want). Use a open source program doesn’t modify the nature of your creations. Your creations are yours.
But, if you make use of some work from other person that has released his work in a certain license, you need to read that license before create derivative works and make a particular use of the it.
Some people that share pieces of animations, effects or similar, release it for free. Others use a Creative Common license.