As long as you don’t change anything like the mortgage term or the amount borrowed etc. then that’s usually the case.
Yes indeed.
Otherwise the lender, by refusing to put them on a new product, may force them into arrears. Pretty sure the FCA would take issue over this.
Off the subject but still on topic I am starting to hear some positive things, swap rates are slowly going down, and lenders are starting to reduce rates (a bit) the general consensus is we may be at the top of the "hump" right now, with things possibly improving going forward.