regarding the first question, here's how i'd do it... it does get the same answer as yours....

abcdefghijlkmnop

imagine that these are the 16 players in a line.

ways of rearranging the line: 16!

now let's divide the teams.

abcd/efgh/ijkl/mnop

when i claimed there are 16! combinations, I made a lot of repetitions.

we must firstly divide by the number of ways the players can be re-arranged in their own, individual teams, because, for example, abcd and acdb are the same team.

each team consists of 4 people, therefore there are 4! possible ways of arranging each team. therefore we must divide by 4!x4!x4!x4!

now the number of combinations = 16!/(4!x4!x4!x4!)

we also must take into account the order of these four groups...

that is to say efgh/abcd/ijkl/mnop is the same as abcd/efgh/ijkl/mnop

the number of ways in which these 4 groups can be arranged is also 4!

for this reason, we must divide again by 4! (and i think this is the answer to your question, you divide by 4! because there are 4 teams)

thus numebr of combinations = 16!(4!x4!x4!x4!x4!) = 2,627,625 --and this is what you thought it was