또 만나요.

It is 'polite' (haeyo-che). It's the standard level for most social interactions with people you aren't extremely close to.

Yes, it's very common to end a phone call with '또 만나요' or '나중에 또 통화해요'.

'또 봐요' is slightly more casual and common among people of similar age. '또 만나요' is slightly more standard and 'textbook' polite.

A small head nod or a slight bow is very appropriate and will make you look very culturally aware.

It's a bit unusual unless you are a regular. Usually, you'd say '수고하세요' or '감사합니다'.

You can say '또 만나!' or '또 보자!'

No, you can just say '만나요' (Let's meet), but '또' adds the 'again' nuance that makes it a farewell.

Just use a general '안녕히 가세요' (Go safely). It's polite but doesn't suggest a future meeting.

It's often a 'social goodbye' meant to maintain harmony, not necessarily a concrete plan.

Yes, but '또 뵙겠습니다' is better for professional emails.

The Romanization is 'tto', but the sound is a 'tense t' (ㄸ), which sounds like a sharp 'd' to some English speakers.

This is a 'plain' formal style. It can sound a bit bossy or like an old man speaking. Stick to '만나요'.