My colleague created a new team using an email address of an organisation different to myself and another 3 colleagues. The 4 of us are now guests and therefore have restricted access/actions. Is there any way for us to become members or for the team owner to change the team to his email address that is the same as ours?
Nope, accounts need to be created as user account in the tenant and passwords you set sent to them and a license assigned. Guests cannot be converted to my knowledge.
If you are talking about free teams setup, same thing, you'll need to invite as members to the org and not as a guest. If it doesn't let you then you'll have to go into portal.azure.com and remove the guest account before adding as member. Keep in mind they will lose any chat history for the account.