1. Don't link the bootsector and the rest of your binary together. It's more trouble than it's worth, and if you ever progress to loading off a filesystem, then you won't be linking them together anyway.
2. You can use LBA addressing in real mode with int 13h (just specify a hard disk rather than a floppy when booting):
https://wiki.osdev.org/ATA_in_x86_RealMode_(BIOS)#LBA_in_Ext...
3. You need to switch to protected mode, set up paging, and then enter long mode.
4. I'd recommend compiling your rust code to an ELF binary, and then using objcopy to create a binary:
objcopy -O binary $input.elf $output.bin
Alternatively, ELF isn't that hard to parse, so you could load it yourself and then copy sections to the right locations with your bootsector.5. OSDev.org is your friend. Maybe get a C-based kernel running first, as the toolchain when dealing with freestanding code is a lot friendlier for beginners
- https://wiki.osdev.org/Protected_Mode
- https://wiki.osdev.org/Long_Mode#Long_Mode
You might be better off starting with 32-bit rust code instead, in order to avoid paging and long mode at first (you'll still need to switch to protected mode)