Yes. A limited company can pay into a director's pension and deduct it as a business expense. No National Insurance is due on it, nothing is taxed on you, and the limit on your own earnings does not apply to it.
A company pension contribution is deducted before corporation tax and is not taxed on you when it is paid in.
No. A pension contribution is an expense, so it can create or increase a loss. Whether that is sensible is a separate question for your accountant.
Carry forward needs you to have been a member of a registered pension scheme in each earlier year you want to use. It does not require earnings in those years, and it does not require the company to have existed.
Not for pension purposes beyond the allowances. For corporation tax, where a contribution exceeds 110% of the previous period's by £500,000 or more, the relief is spread across future periods.
Your own contributions would be capped near that figure. The company's contributions are not capped by your salary.
Agree the contribution before your company's year end. The amount depends on your allowance, any taper and what you can carry forward.
Your first call is with an Account Manager and is at no cost to you. Tell us what is on your mind: a pension you have lost track of, a fixed rate ending, a will you keep meaning to write.