Uz tikšanos!

It is neutral. It's safe for almost any situation except with very close family or in extremely formal ceremonies.

Yes, it's a very common and professional way to end an email to someone you have a working relationship with.

'Tikšanās' is the name of the noun (nominative), and 'tikšanos' is the form used after the preposition 'uz' (accusative).

Yes! It's used generally to mean 'See you later', even if no specific meeting is on the calendar.

In very casual texting, yes, but in speaking, it sounds incomplete. Use 'Tiekamies' instead if you want to be short.

It sounds like 'uo'. Think of the word 'duo' but blended into one syllable.

Yes, 'Atā' is the standard casual 'bye'. 'Uz tikšanos' is slightly more 'polite-casual'.

You say it whenever you are leaving someone, regardless of the time of day.

Exactly. It's the closest equivalent to the friendly English 'See you!'.

Then use 'Visu labu' (All the best) or 'Uz redzēšanos' (which is more distant).