Reddit mentions of Park Tool (109917) HCW-5 Lock Spanner

You have a loose crank arm there, and what looks like probably a loose bottom bracket too (the part at the bottom of the bike that the crank arms attach to, it spins).

It's very possible that that bottom bracket doesn't need replaced, and just needs taken apart, cleaned out re-lubed and tightened. Then you would clean up those rusty crank bolts with barkeeper's friend to make them shiny again, and put them back on pretty tight.

It depends how expensive the bike is. If it's a $300 or less bike I would bet relubing and tightening the bottom bracket and then just tightening the crank arms would put it back to working like new.

You'd need a bottom bracket wrench to remove the bottom bracket, and a crank puller. For both those tools that's gonna be about $23. These are cheaper ones but you will only use them once so it's fine.

Then you need some marine grease at Walmart for about $4, and some bar keepers friend (at Walmart or grocery store for about $3).

This is a total of about $30 to fix your bike on your own.

You could follow a video on removing the crank arms
And removing and relubing your bottom bracket.

You would take the bolts off your crank arms, pull both crank arms off with the crank puller, and then remove the bottom bracket. You'd clean it out real good with rubbing alcohol or brake cleaner, and then relube it with marine grease, and then tighten everything down. Then you would clean up those rusty crank arm bolts with bar keepers friend and an old tooth brush, and then tighten the crank arms back on. Bike would be good as new for $30. So long as you're patient, careful, and follow the videos. Look around online for things if your not sure.

If you have access to a torque wrench that would be great to follow torque specifications, but you can do without if you follow a video. I mean, your bike will be much safer afterwards than it is now. Fixing it well (instead of perfect) is better than not fixing it at all.

If you are not a d.i.y. fix-it kind of guy, you can go to a bike shop. Not sure how much they will charge. I wouldn't know, I rarely go unless I'm buying a bike. I only wrench at home 🔧

My first fixed gear! Yeah all you need is a cog and a lockring, make sure the measurements are the same! buy a lockring wrench too and you can do it yourself.

Compatible Cog, Lockring, Wrench(spanner)

Not sure what you mean by strange bottom bracket - it looks pretty standard to me. You need something like this to remove the lockring and a large spanner should be able to remove the actual shell.

As for the cranks personally I would just take an angle grinder and cut the axle near the cup, OR after removing the bolts just take it for a nice ride up a steep hill and with caution knowing that the crank arm will fall out. If it doesn't fall out after your ride go again or literally give the crankarm a good kick with the frame on the ground (has worked for me before).

Unsure what exactly your post is asking. Please clarify?

You should check your threads first before considering getting a new rear wheel.

If the threads are alright, go ahead and tighten everything down (as recommended by bikesdirect). First the rotafix method to tighten down the cog. Then use a lockring tool to tighten down the lockring.

If the threads are trashed, you can easily find a wheel that is less than $150 (assuming you mean this since >150 means greater than $150). There are some typical "favorites" on FGB like velocity deep v or mavics.

Please note that the links provided are just quick-n-dirty suggestions. Some of the Park Tool sets would cover a lot of these things, but when building from frameset up... you may want to seek out a shop with the odd tools you might only use once or twice in your life.

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Aside from the standard tools, like box wrenches, cone wrenches, Allen wrenches (aka hex keys), flathead and Phillips head drivers, Grease... you'll need tools for:

• seating the fork race
  
• installing the bottom bracket (or press fit or one of a few other types?)
  
• cutting cable & cable housing
  
  In addition, you may need:
  
  
• adjustable crescent wrenches
  
• facing and chasing the BB threads
  
• at least a 5 nM torqe wrench, perhaps a 6 nM as well
  
• chainwhip tool
  
• spoke nipple wrench
  
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  I'm sure you could "get away" with less, or perhaps the Park Tool Advanced Kit but there's a reason for these tools. Good luck.

Quick tool question hopefully. Looking to further flesh out my bike tool box with more fixed-specific tools so that I can work on the bike more independently. What lock-ring tool(s) would be the most versatile to pick up? Is this one the go-to? I have a Crew District, with the stock wheelset and have had bike shops swap cogs and freewheels for me up until now, but want to get a bit more hands on with it. Also, the freewheel I currently have on their is an ACS crossfire, fwiw. From what I am seeing, that one needs it's own removal tool, also? Or do there exist more universal options?

I've got a park HCW-5 tool. If it's a stubborn ring, the three tooth end can grab three notches at once and I've been able to pop off all lock rings without too much difficulty. It's cheap and effective.

Park lockring tool is the standard for this kind of stuff. I like the Hozan version of the tool myself since it's forget but the park one works fine. Nashbar and other discount shops should have a similar one too.

loose bb cup and cone are still made, but thats besides the point.

a lockring spanner would be the best route, a flat head & hammer would work, but you likely damage the lockring

Oh, for that, you want something like: https://www.amazon.com/Park-Tool-HCW-5-Lock-Spanner/dp/B000C17KRI

e: aaaand you already found it in the video