My 24 month contract ended with Three yesterday for my iPhone 4, can I just buy a pay as you go Sim card for any network and use it?

Will all the apps etc work okay if I find a Pay as you go bundle with unlimited data?

Has your iPhone been unlocked?

I would guess the phone will be locked to Three as they do with all their phones, you will need to contact them and probably pay a fee to get it unlocked.

After that you can put any SIM in it and yes all the apps will work fine if if you have no SIM in it.