The bottom bracket will be 68mm wide and need an axle around 115mm long. Those chainrings are very good with a price to match. You may do better asking on here or the London fixed gear site https://www.lfgss.com/microcosms/551/
to see if anyone has chainrings or chainset in better nick than yours.
Lovely bike. Should be a trip to your local bike shop to get the parts suggested unless you have the tools and knowhow especially if changing to more modern parts which need different tools. The handlebar stem looks very high, is there a minimum insertion mark visible?
"repop" is a new one to me! It's a "New Sintex" so I'm guessing late 90's as Neuron came out about 1995. It's had a couple of years as a Dura Ace 7700 bike but now it's up to 7800 and approaching 4,000 kilometres. The forks look better on a complete bike I think... This photo doesn't do it...
Re: Michael's Jackson
Take the road less trodden, forget the Shimano retroclones. Seek out the lost lamented deities of the eighties. Suntour Superbe Pro.