Legal Question in Real Estate Law in Illinois

Any time there is a mortgage there is the potential of loosing the property. Therefore (you) have affected the rights of the other owners. The bank would want clear title in the event that there is a default on the loan - a share is not what banks are interested in.

Therefore:

A mortgage is compromising the rights of those not on the loan without benefit to them.

The bank wants a "nice clean foreclosure" in the event the loan is not paid off. It does not want to fight with others, even taxing authorities, who might have rights.

Yes, all must be on any loan -against- the property. Please notice that even you used the word 'against'.

You do not all need to be obligated on the loan, but the bank will want a mortgage on the property. So, it is possible that less than all the owners would bind themselves to repay the loan (sign the Note), but all would have to bind themselves to put up the property as security (sign the Mortgage). If not all the owners are benefiting from the proceeds of the loan, then they are taking a risk that the property will later be foreclosed and they will have lost their interest in it.

Normally yes and the owners should enter into an agreement as to how to manage it: how to contribute toward payments (PITI), what happens if someone doesn't, etc.