The UN54 will be compatible as a replacement - just make sure you order the correct axle length. if in doubt measure with a ruler.

Assuming you have worked out the 68 x 113 correctly (it sounds correct) then probably all you are worrying about is the taper fit and the thread into the frame. The taper will be JIS which is Shimano compatible, and the thread will be English standard so yes the Shimano UN54 will be correct.

The book I read recently by Richard Ballantine suggests you go to a local bike shop for this task.

Personally I like a challenge, so if you are like me you won't be disappointed :)

Different bottom brackets have different tools you need and can indeed have threads that go in the opposite direction to the current standard (though this is rare). I suggest you read up on them, various sites and video sites are useful for this.

For fitting this you will probably need:
a socket set
an adjustable spanner
a crank removal tool
a Shimano Bottom Bracket Tool

Needs change per bike / components etc, but these are the ones for my bike, make sure you check before buying.

I have before now had to bolt the tool to the bottom bracket to prevent it from slipping, these are notoriously difficult to remove especially after a good few years of weathering and dirt.

Have fun!

That means its a 123mm BB with a 68mm (English) shell.

The UN26 is just a lower specification Shimano (the fittings are the same). The UN54 in 123/68 format would be a perfect replacement. Or there are plenty of other Shimano compatible BBs available in 123mm / 68mm JIS square taper. They all conform to the same couple of standards.

That is a 68mm (English) bottom bracket shell with a 120mm axle and JIS (Shimano compatible) taper.

So you can replace it with the UN54 or any similar Shimano or Shimano compatible BB. Just make sure you order the 120mm version with 68mm shell.

Don't do it. The chainline won't be straight, your chain is not meant to move side to side on a singlespeed and it could skip off which is nasty especially if you're riding fixie.

Wiggle sell Token bottom brackets which are available in 102mm and 103mm. I used one myself and it's good. Not expensive and you can get either ISO or JIS taper. Your Suginos probably need ISO taper.

Probably, it's only 0.5mm difference, you'd never be able to tell. I'd do it on my bike.

If you remove the old BB it should be stamped on the outside.

However as it's a Scott it'll be English standard (ie 68mm) and will be JIS taper (ie Shimano compatible).

So really all you need is the length of the axle. Get a ruler out and measure it from the face of the square taper on one side to the other.

OK, first up 113mm is probably too wide for a singlespeed, you would have a very wide chainline. More likely 107mm or 102mm would be better. There is a lot of information online about measuring your chainline but in essence you want it as close as possible to the frame for a singlespeed.

Second, Shimano BB's use a JIS taper, but european square tapers have traditionally been an ISO taper. Stronglight (a French make) changed from ISO to JIS some time ago so it does depend how old your Stronglight cranks are as to which you need.

I suggest you google "Sheldon Brown JIS" to get more information. They will fit but the wrong taper might make your chainset sit too far out.

If you need ISO then look for Token bottom brackets, Wiggle sell these in ISO and they are good value.

The UN54 will be fine, it's just a model number. Make sure you get another 113mm obviously. The thread is standard, so is the taper (JIS standard) and the shell width will be 68-73mm which the UN54 will fit.