Enseguida.

Both are correct, but 'enseguida' (one word) is preferred by the RAE and is more common in modern writing.

No. 'Enseguida' implies the very next moment. Use 'mañana' or 'pronto' for things further away.

It is neutral. It's perfectly fine for both a business meeting and a dinner with friends.

'Ahora' means 'now' (the current state). 'Enseguida' means 'immediately' (the next action).

Yes, in some regions you can say 'enseguida de' to mean 'next to', but its temporal meaning is much more common.

The most common way is 'Vuelvo enseguida'.

'Inmediatamente' is more formal and longer. 'Enseguida' is more natural in spoken Spanish.

Yes, it's very common in professional emails to confirm you are working on a request.

It's a polite way to acknowledge a customer's request and promise quick service.

When used as 'enseguida que', it takes the subjunctive if the action hasn't happened yet (e.g., 'Enseguida que llegue, te llamo').

Yes, it is universally understood, though some countries have local favorites like 'al tiro' or 'ahorita'.

It's better to say 'enseguida que' or 'nada más que'. 'Enseguida de que' is often considered redundant.