Yes I recognise that – it’s a freewheel as you say. The spined tool to remove it is about a fiver (I have one you could use if you can visit me in Nottingham!). Or take it to your local shop – it’s a 10 second job to remove it with the right tool! The whole lot comes off leaving your bare hub which is threaded. Then you should be able to just screw on a singlespeed freewheel – White Industries (£70ish), Shimano (£20ish), Dicta (£8ish). Chainline might be a bit of an issue but you can play with that at the chainrings.
And I don’t think you can “convert” that 7-speed – if you try dismantling it you’ll see a step in the body of the underlying freewheel – some of the cogs are splined (not like a 9-speed cassette) and some screw on… Not worth the effort, buy a freewheel!