Since you have a US address, this makes things a lot easier - just keep your bank accounts and credit cards linked to that address. I would still recommend auto-pay, but just make sure to move enough money from savings to checking.

It definitely is ideal to keep your cards open; I have several UK-based friends who do that. The credit card scene in the UK / Europe is horrendous compared to the US; just as an example, the best credit card that offers no FX fee comes with 0.25% cashback. Most travel credit cards with no FX fees offer no rewards.

For general spending, it's not easy to find a credit card that gives more than 0.5% rewards; the best debit card (Chase) used to offer 1% cash back but this is ending in April.

TL;DR: It's doable, and definitely recommended.