A: As this is not covered in the partnership deed and there is nothing specific about this in the Partnership Act 1890 either, the decision is in your hands.
Under the Act, all partners are deemed to be of equal standing on the basis that they are all jointly and severally liable.
However, one partner has to agree to stand as a 'precedent partner' for the purposes of signing the partnership's annual tax return.
I suggest you decide between you that the partner who takes on this responsibility should also be entitled to adopt the title of senior partner.
That said, as all partnership decisions have to be agreed unanimously by all the partners, being the senior partner will amount to nothing more than a complimentary title as it does not offer any real power.