What do I need to replace my singlespeed freewheel cog? As I learned in this question, the cog of my freewheel are damaged and should be replaced.

I've been searching for some information but I'm still not sure of what I need. At the beginning I though I just needed to search for a cog like this with 1/8" like my chain:


But reading the description it seems like it's only for fixed gears, so I was completely worng. Searching for more items under the single speed category in the website everything looked like that.

What do I need to buy as replacement?

This is how what I have now:


As tools a I just have the basics, when i search for freewheel remover I see hundreds of different things like this:



 ...

How can I know what I need?

Update with photo of the wheel:
Park tool has a guide to figuring out what type of free hub/freewheel you have, and what tool you need to get it off. 

https://www.parktool.com/blog/repair-help/determining-cassette-freewheel-type. 

With that knowledge you should be able to to figure out what type of replacement freewheel/spocket you need (or two, as you have a flip-flop hub). 

Update:

Also see the Sheldon Brown page on Freewheels.

Depending on what the freewheel thread turns out to be, you should be able to get a replacement freewheel that has a more standard lockring. 

You might consider creating a 'bodged' tool to get the current freewheel off. You might be able to 'drift' the lockring loose by tapping the ring around with an old screwdriver and hammer.