on a visa exempt entry in Bangkok you go to IT Square Laksi Plaza on the 3rd floor to get an extension. There are copy shops next to the office to do copies, photos etc.
You go here
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As far as IF you will be questioned comin' in visa exempt (there is no VOA for Britz) that is just down to luck of the draw. Bangkok has a higher chance of questioning you, but people have been pulled aside in Phuket too.
Having a tourist visa in your passport is no guarantee that you'll skate thru without questioning either, all it does is IF you're let in gets you stamped in for 60 days.