If you've got a steady hand, the right tools, and a properly- equipped work area, sure.
Yes. Chip components and SOT transistors are relatively easy to deal with. It's when you start working with ICs that it gets dicey, and starts working up into the realm of $400-$700-$multi-thousand dollar surface-mount rework equipment.
No, but they're available in plenty through channels such as Allied, DigiKey, Mouser, et al. They're also widely found at surplus electronic component dealers.
Definitely worth learning at least enough to do testing and repairs, considering how much of commercially-made ham (and land/mobile) radio gear uses surface-mount stuff.
Happy hunting.