The C65 ROMs are largely based on the C128 ROM, so I believe it should support burst mode when in C65 mode, but I can't immediately confirm that.
Regarding accelerating the byte-by-byte routines in the ROM, I looked at making it pass a pointer to the sector buffer and/or copy ~30 bytes at a time in the little transfer area it uses at the top of the 2KB colour RAM. I got part way through, and ran out of time. The nice thing is that this fix would be totally compatible, and also would work on a real C65, to give about 5x - 10x speed up for LOADing, from ~1KB to more like 10KB/sec. On a MEGA65 it would go from about 16KB/sec to around 100KB/sec, which is currently the limit of the SD card interface (although I plan to improve the SD linear read speed to ~1MB/sec).
I think the rest of the questions have been answered by others?