Q1 - Don't understand
Q2 - Legal owner may or may not be the registered owner. It might be held in trust by the registered owner for someone else. To nail down thel legal ownership issue, you would need legal advice as to whether the registered owner should hold it in trust for both the registered owner and A N Other.
Q3 - if they want to and if the bank more importabtly want to.
Q4 - bank might not give mortgage on the one salary. however, if they are taking second income into account, they will need some more documentation signed wherby the person not named, will not interfere with any repossession in the event of repossession being necessary.
Q5 - You need to work these out for yourself. Why do you not want to be named; Why do you not want others to know that you are the owner?
Q6 - lender will want to know why this arrangement is being propsed and will need to be satisfied with it.