First of all, stop lumping everything into one pile
1) partitions, gpt and mbr
Just search for it. These are nothing more than 'partition index -> offset, size' + legacy crap (MBR) / overengeneered crap (GPT).
Repairing them boils down to finding surviving file system signatures and
making new MBR/GPT
2) bootloader
Generally, not worth repairing. Live CD & grub-install are your friends. Just be careful that partitions are correct, so you do not clobber some other data
3) fsck
File system repair. Details and practices depend on what file system you are repairing. So focus on something specific.
4) chkdsk
Physical damage. Learn about SMART to detect failing drives before they fail and ddrescue