1. Let's suppose two players want to trade. One needs to get from a point to b point and other from c to d. their paths cross on one spot let's name it "e". Can first player get to "e", stop, second player get to e, they trade, and then both of them continue to their goals (b and d), or does first of them has to stop at "e" until the end of the turn in order to trade (so that second player can pass by and trade)?

b

l

a -------------------- e -------------- c

l

d

2. If Other world card that playr return to Arkham immediately (other world phase), does that mean that the next turn monsters around gate immediately attack player, or can he close the gate next turn without getting attacked:

4. phase: returnig to Arkham because of a card that says so

next turn

2. phase (movement) : attacked or not attacked by monsters?

3. phase close gate

1) All movement must be completed before the next player moves so if you stop and someone else moves, you have zero movement points. So the first player must stop and end their turn in the street in your example.

2) Yes you must fight or evade those monsters in your next movement phase. The option not to is removed once a new movement phase begins.