1. Yes. About " solder screen " maybe you are talking about soldermask. The soldermask has very low inquiries , even I ca do it.
3. A4 and bigger size it is possible, but please note that if you have more pcb's on A4 can not be " panelized" . The best is to be manufactured piece by piece, in order the have best quality of boards.
4. No. For double side boards you will make the vias connection. For double side are required .brd ( Eagle files)
I hope that may answers are very clear for you.
Regards from Romania,
Thank you for your answers I will consider sending my pcbs to you when I will need them. I am planing to make a 2k smps and will need a prototype. But if our fellow members may want to build it then I will ask for more.