Recently I helped replaced the stock pipe on air frame with a tams pipe on a 180 sized jet (I think it may be a skymaster dragon? or feibao?) for and took out the stock Chinese pipe . The Tams pipe certainly was higher quality but the thing to notice was that the tam pipe was 10m smaller in diameter. After flying it was clear that the jet gained some speed I would say 10-15% faster. It was also clear takes off took more runway (less thrust?).

This has me thinking, do smaller diameter pipes increase air frame speed? I suppose Its similar to a garden hose, decreasing diameter increases pressure and speed of the water. I'm assuming its raises temperature inside the pipe so the pipe would need to be of high quality to be able to handle the extra temperature.

On some of the skymaster jets are not coming with 300N options, in these the the 300N has larger diameter? is this to slow the turbine down vs a 200N which has a smaller diameter pipe. What if using he 200N pipe on a 300N turbine would that increase speed of the 300N?

Kind of makes sense. Smaller diameter means less expansion, thus higher velocity.

Bigger pipe = more static thrust but lower velicoty
Smaller pipe = Higher velocity lower static thrust.

So smaller diameter also needs to be stronger.

It's not EXACATLY linear - see the Wren "augmenting" pipes. There's actually an optimum shape that starts at a given diameter, expands to a set diameter and then is constant beyond that. Kind of like scavaging exhaust from engines. There's a formula for it somewhere on these forums. Actually is pretty easy and straight-forward if I remember right.

Cooler tailpipe temps with larger diameter...
The biggy is static thrust, most models (scale) are over powered for most people's throttle use! For a sports jet there is an optimum, for scale run as large as practical and its usually right.
142-180 motors can share a pipe, 90mm is my go to size, 92-95mm 180. 100mm 200 big block

Most people set the tailcone to tailpipe distance wrong and this affects thrust more!

yep

Besides being the general rule 25mm for most tailcone to tailpipe what is the correct distance?

There is a book right there!
Turbine tailpipe design has the biggest influence, pipe diameter and design (bellmouth design) Small lip flared tailpipes, should have a smaller gap.
Best advice is from your turbine manufacturer. Like you say 25mm is a good starting point on single cone byepass system installs. The old P-80 type with twin cones needs a larger gap measured to the outer 'short' tailcone-around 50mm.
Many just install the turbine where it sits. As turbines have got longer, its more difficult to get the turbine far enough forward.

Models like the Flash/UF that have been around since 2006 need the 3mm front turbine rail vertical former cutting flush to the rails so a JetCat turbine can be moved far enough forward.

I'd be very careful with that rule of thumb. I don't think that is necessarily correct. You have to look at the overall picture. What are you trying to do with the pipe? You want to maximize speed? You want to maximize engine cooling? Do you have a bypass? A lot of it is trial en error too. The larger the pipe diameter, the closer you can bring it to the tailcone.