All of europe is having similar issues. Many eu countries and the uk have increased their rates to try and stop inflation and as a result fewer people afford mortgages driving prices down. But the issue in some places is that builders have stopped building due to increased costs and as such the offer is lower. No clue how things will play out.

Depends but overall the US rates put pressure on euro and generally all other currencies. In my country, which does not have euro, the last hike of the US rates got the currency to drop over 2% (which is already super weak). This means that our central bank will need to bump its rates even further.

There is a relationship, yes, but it’s fairly indirect. More important is simply that the ailments of the US are suffered by the west in general. The UK raised its interest rate this week, by less than the US, but with a feeling that a much larger rise will come in August.