Unless someone has laced a freehub to a 27" rim (unlikely), it's a freewheel and not a cassette you need to remove: freewheels contain the clutch mechanism that allows you to er... freewheel and screw onto the hub; cassettes don't contain the clutch (the freehub does) and slot onto the er... freehub.
Yes, the freewheel removal tool is specific to the freewheel: have a look for the brand (and the number of slots in it to accept the tool) and search for that.
Freewheels (multi-geared or single speed) aren't rim specific, they're hub specific: specifically the threading. Most likely you'll have an ISO threaded hub: have a look on the existing freewheel.
Sheldon Brown has a useful glossary, if you're unfamiliar with specific terms.
Unless someone has laced a freehub to a 27" rim (unlikely), it's a freewheel and not a cassette you need to remove: freewheels contain the clutch mechanism that allows you to er... freewheel and screw onto the hub; cassettes don't contain the clutch (the freehub does) and slot onto the er... freehub.
Yes, the freewheel removal tool is specific to the freewheel: have a look for the brand (and the number of slots in it to accept the tool) and search for that.
Freewheels (multi-geared or single speed) aren't rim specific, they're hub specific: specifically the threading. Most likely you'll have an ISO threaded hub: have a look on the existing freewheel.
Sheldon Brown has a useful glossary, if you're unfamiliar with specific terms.
"A picture is worth a thousand words."