It’s located in Midwest City Oklahoma, rent for this house works easily be $850/month.

If a mortgage has a deed restriction, not allowing short-term rentals that is not imposed by an hoa or a city government how hard is it to get it removed?

I'm not sure what the markets are like in Edinburgh or London, but I would look into house hacking in one of those cities once you know which one you'll be in.You definitely can invest in rentals in the US remotely, there are plenty of investors that do.

They are really changing the shape of the city and it may become incredibly expensive to buy out there soon due to lack of housing.

If you're okay with that, you can buy in just about any MIdwest city, just make sure you know the landlord-tenant laws.We've broken down the City of Detroit's 183 Neighborhoods, can share if interested.

You could reach out to a few Property Managers in Salt Lake City to see if any of them would be able to give you advice for the area, as they would be familiar with the region and what to expect from the investment! 

Overall it is still a very good city to invest with solid returns.

Quote from @Jules Aton: I started investing in my late 20s during early 90s in up and coming inner city neighborhoods.

In a city like Philly, you will face many challenges - you need to learn the market and know the neighborhood and the block and make sure all of your numbers are within reason, you need very reliable contractors, you need a to understand the permit process, you need to be familiar with market expectations. 

I started getting into some Facebook groups couple of days ago, I'll definitely look into RE events, I know there are few that takes place in the city most of the weekends