What surface finish is better if the board is expected to go through frequent temperature cycling (-40 °C to +85 °C) and mechanical shock? ENIG or HASL?
ENIG is better because of its high thermal reliability which helps in maintaining strong solder joints under thermal stress. It provides better resistance to pad lifting under vibration and shock due to its nickel layer. Its surface is quite flat and smooth which avoids stress concentration and gold layer protects the nickel from oxidation.
There is not a straight forward answer to this, it depends on how frequently the connectors are plugged in and pulled out. It will also depend on the size of the board and the amount of open space available. Generally it is better to keep BGAs away from connectors (as far as possible) mostly at the centre of the PCB since that is the region expected to be the farthest from all four edges of the PCB which are expected to be under stress. If the connectors are carrying impedance traces then the length of those traces are also critical, therefore the distance then will be governed by what is the maximum allowed length of those impedance traces.
Probably the best way is to use Aramid/Kevlar reinforced laminate. Not cheap but definitely tough. Can also use external backer boards if there is enough room.