Since u are starting fresh, u shld bleach the rock to kill all the unwanted pests that come with the live rock. If the crab is hairy, most likely will eat ur corals in future.
1) top up with filtered water as salt does not evaporate. However, if u have a skimmer, u will still need to monitor the salinity as it will go lower with the waste being skimmed out.
2) u need not remove them if they are not pests. May even help u to eat diatoms during the cycling period
3) yes, chillers will be recommended. Lps and soft corals are usually hardy
4) depends on u. Most impt thing is u must measure the water parameters. Corals first then fishes. Go easy and slowly. Patience is a virtue