Would it be worth it for me to go through a book of 3 move mate puzzles? or should I do something else, also can someone give me a list of openings I should learn as I find that it is my weakest point of the game.

do you mean three half moves (mate in two)? or mate in three puzzles?

openings can be very fun. the thing is is that you can almost never 'learn' enough about the openings. learning the moves that charaterize the openings is very fun. memorizing variations is not so fun. even though most people here will tell you to stay away from openings, every one of them has learned them. im not that strong but i know a lot of openings. just learn the fun parts like the names and a few moves. just dont go too deep.

Mate in 3 (You move, they move x3)

As with the openings, I think Im just going to choose to learn all the major ones for white off of e4 and then d4 and progress from there.

A friend told me that it would be better to do tactical problems like the ones where you to have to find something to get you up a pawn etc.

Non-mating tactics puzzles are probably best, since those types of situations come up more often in actual games. You need to learn to spot knight forks, bishop skewers, queen forks, etc instantly when they come up in your games.

--Fromper