@BooksAndChooks
Re the £85k, yes that is true. However, you can get round this by putting your money into different accounts. Also it is per person, so your partner/spouse also has this 'allowance'. Plus if you save with NS&I, the protection is much higher.
See www.moneysavingexpert.com/savings/safe-savings/ for a full explanation.
Obviously investing the money is a risk, as you don't want to have to remove the money if it's not grown as much as your mortgage rate. But if you have a very low interest rate mortgage, you could probably beat the rate with cash savings, which is all you need to do and should be easy if interest rates continue to rise.
We're on an old lifetime tracker and have spent much of the last 15 years paying under 1% interest on our mortgage while at the same time saving in premium bonds, regular savers and current and savings account.
At one point I was getting nearly as much interest on the £2500 in my Nationwide current account than our mortgage was costing, and that was without counting other savings we have. Sadly this has now come to an end and it's likely we're going to pay off the last of our (admittedly small) mortgage next week, after 'premium bonds prize day'.
Don't know the answer to your third question, and I suspect that is 'it depends on the T&Cs of your product/lender'.
But if your fix is around 1% or so, I'd not worry so much about that, as you'll be costing yourself money by overpaying. The only caveat is that if you ever find yourself in a position where you need to claim universal credit, you'll be expected to live on savings until they fall below £16k, which you wouldn't do if you'd overpaid your mortgage, so it's worth thinking about how likely it is that could happen.