Travelling between UK and Turkey with 2 passports (each is visa free for one country only), which one shall I show at airline check-in / immigration?

Question

I would like to have some advice. I have 2 passports, travelling from UK to Turkey and back:

• passport A gives me visa-free to enter Turkey for 90 days;
• passport B needs visa to enter Turkey, but it has my ETA visa for entering UK.

Question:

1. I believe I would show passport A when check-in at Heathrow;
2. I believe I shall use passport A to enter Turkey immigration both in & out;
3. But, when I check-in at Istanbul airport (Turkish airline), shall I show them passport B (with UK ETA), or just show passport A is ok? Would that be an issue if I show both A&B to airline?
4. Any idea which passport information shall I fill when buying the Turkish airline ticket? But given no border control exiting UK, would that be an issue if I fill passport A but not B?

I google and it says Turkish accept dual citizenship. Anyone has similar travelling experience in Turkey or even other countries (different passports have different visa requirements).

Thanks in advance.