something has gone wrong with my sewing machine but I don't know what!

[MostlyCake]

Help! I changed needles on my singer 201k machine and since doing that I've snapped two and bent a third. I've replaced the needle again and now the back of the sewing is all loopy and loose.

what's gone wrong?

It looks like the upper thread tension is set far too high; you shouldn't be seeing the thread from underneath pulled through. This would snap the needle too. Check the tension and check that it's threaded correctly. HTH

I would completely rethread, top and bottom. Make sure you are in the right place at the tension discs, it can be easy to miss the right groove.

Have you got the needle in as far as it will go and the right way round - flat side to the left on my 99K.

DD(8) can now thread the 99K here most of the time, if it goes wrong I completely start again and it is fine, generally her problem is the tension disc area.

Here is the manual foc in case you haven't got it.

www.singerco.com/uploads/download/1297_201k.pdf

This might sound daft but check the needle is the right way round. I would re-thread both top and bottom, check the bobbin is right as well and give it a clean to get rid of any lint. Also check that the thread is clicked in properly on the tension disc. It's different to a modern machine.
Something similar happened with my 201k. I called repair man, who took one look and turned the needle round. I had it in with the flat bit at the wrong side