1) All mods have set stats that can roll on their primary so the primary per slot talk is based on which stat that particular shape of mod can roll. So Speed can only roll as a primary on the arrow mods, not the cross or triangle or any others so people say speed arrow (over offense arrow or crit avoidance or whatever). Likewise crit damage on triangle mods are usually good but you cant get them on squares.
2) Sort of, mods add power and power adds to ship strength but its not linear. Giving a fleet pilot more speed doesn't give that speed to their ship. Each ship gets stats at a certain rate regardless of how the pilots stats are allocated, but giving them mods does increase the power of ships you just can't decide which ship stats to boost.
3) You cant be battled when you are battling someone, so the long delay is there so you can't lock yourself into a position for 15+ minutes by repeatedly battling.
4) The cap is stupid, especially with new tank level gear added old rancor gear should be upped to 5 (or no limit at all)