I looked and couldn't find any info on how to manipulate my have, wants and collection. Is there a certain web browser I should be using or did I miss a check block somewhere. Also, is there any way to save team builds for later?

When you look at a unit, there are three sets of up/down arrows beneath the picture (or where the picture would be, for units that don't have one).

Keep is the figures you have in your permanent collection. Have is for figures you have to trade. Want is figures you want to trade for.

You can't save teams, but that feature is being worked on.