Yes, because your existing mortgage agreement, in the fine print, says you must live there and not rent it out. You might not need a BTL mortgage as such, but you must ask your lender's permission to let, which amounts to the same thing.
No, you can just do it, but if the lender finds out, he could get angry enough to make you wish you'd been good.
What makes you think any would? Whether CGT applies does not depend on what kind of mortgage is involved. Under current rules, you can let for at least 3 if not 6 years without CGT becoming a problem.
If no to (1) or to (2)? I thought you said you have one already. By getting permission to let, you would avoid having to scan the market for impaired-status BTL loans. But with plenty of equity you could always go for a non-status loan, but it'll cost more.
A joint mortgage with whom? It can get messy with CGT unless it's with your spouse. It can get messy even then.
Well, you're the local expert. It may well be a good time to let even if it's not necessarily a good time to buy to let, or to borrow against property which is at risk of losing value.
Yes, and mortgage loan interest (but only for that part of the loan used to buy the let property). And insurance, repairs, etc.
But you'll be in "some dirt cheap East European country". What will you be doing there? Would you expect your UK property to generate enough rent not only to pay the mortgage but also fund your lifestyle over there? Do you think you'll be able to work there, or just bum around?
It will also mean your agent will have to deduct income tax from your rental income.