Linux initializes all general purpose registers to zero. It's not documented AFAIK, but should be reliable - it has to init them to some value anyway to avoid leaking kernel state. So you can get away with:
The load address stays constant unless there's some magic GNU extension header to enable ASLR. If we could get the code loaded below 64K, we could save another byte by using SI instead of ESI; however this doesn't work by default, you'd have to run 'echo 0 > /proc/sys/vm/mmap_min_addr' as root first.
Yes, but only in 32 bit mode. Not that it matters, except for the hypothetical future processor or Linux kernel that is no longer compatible with that :)