1. I am not an expert, but it might improve compatibility to some degree, in that it may be more forgiving with refresh rates that are far off of an even 50/60Hz, but I don’t see any reason that it would provide any compatibility with the jittery sync we see with the NES and SNES.
2. No. The TX chip in the OSSC conforms to HDMI 1.4, and it will blackout like it does with every other HDMI device/display. The only way you might survive mode switching with no lag is if the OSSC could gain compatibility with HDMI 2.1’s QMS, and only if you applied line2x or line4x to both 240p and 480i, which is not going to be ideal due to the bob deinterlacing.
The alternative would be an FPGA video processor, not unlike the UltraHDMI, that can be configured to perform framerate conversion and scaling to continually output at a preset resolution and framerate.
3. Looks like FreeSync over HDMI was implemented back in 2015, but using a vendor extension to HDMI, so you would need specific support for it on both the OSSC and your display.