Looking at 'a.' you can use either 'with' or 'for' as the player is with the team that he plays for.
Likewise with 'b' but note that if you do something during a two week period, than you do it for that time, or at least regularly through that time. However 'in' means only that something happened - possibly only once - in that time. So you would say 'During the Mesozoic era the earth was struck by several asteroids, but only once in the twentieth century.'
With 'in' and 'into' we use 'in' for position and 'into' for movement. So you have a dip in the river, because 'dip' as a noun means a short swim, which you do in water. However when you use 'dip' as a verb you use into because the verb means 'to insert briefly and withdraw' as in 'dip a toe into the water'. Because 'dip' as a verb contains movement, you dip into something, but with the noun you take a dip in it.