1. What to answer for: How many employments or directorships did you have?
6 and 2 3's here if you have had no salary no need to complete the page or complete and enter no salary - doesnt really mateer which route you take practicably spekaing.
1a. If I answer 2, it is asking me for ' PAYE Reference' that we don't have as there is no income or salary or dividends. What do I do in this case?
tax return box by box notes are always your friend - rather than try and speculate always check the notes box (you may need to download - onlije notes rae reidiculously pants.
If your employer does not have a PAYE tax reference, write ‘None’ in box 4
2. What to answer for: Were you in a partnership?
ok bit of an aside
It is quite worrying that you don't fuly know the diffference between partnership sole trader and limited company - there are so many situations where forms are sketchily worded and you want to esnure you keep everyone else right.
Limited company is a limited company - you are not "self employed" yoursleves as your company is a separate legal entity of its own you are directors and sharholders and thats your income source from the company - with regard top any question have one hat for you as the individual (not in business) and one hat for teh company that is in busines. Having said that some stupid insitutions may have a combo form - if its unclea always ask whoevber has issued form and say i am company director is this the right form and how do i complkete on that basis.
Partnership is for individuals who are "in self employment" in their own names (with others) - so you would completely iognore all refernce to partnerships and sole trader as you are neither
2b. If I answer 1, it is asking me for 'Class 4 National Insurance Contributions (NICs)' details. We did not have this nor aware whether this needs to be done?
you will tick no to both sole trader and partnershp so class 4 or class 2ni wont come into it preumably this is sub question after you havce incorrectly said yes to partnership being applicable