How many actions can you take at each point? Would I be able to do lore and then a fight or would I have to move off the point and then back again?
Under normal circumstances you can do any or all of the actions at a point while you're there.
If there's a Fight, you generally have to complete that (or have it marked from an earlier visit) to do any other action.
Page 11 of the rules covers actions. Often (but not always) taking an action at a point will cause the Realm Clock to tick - which usually means something bad is getting more imminent.