It is correct that you can't make the mixer window fixed height, that's not how Reaper works. The window size is the boss and the mixer has to conform to it.
However, OP is asking how to make the
fader fixed height. This is a much more complicated question than it might sound, as the method will entirely depend on the theme. Fixing the height off the fader will be easy, but
something else will have to change size when the panel resizes, or do a 'toosmall' crop. This would possibly be a very convoluted re-write of existing WALTER, but the effect would be to mirror the lack of resizing functionality on beginner level WALTER themes. So if you ever wanted to learn some WALTER, this would be a good second project.
Your first project (EVERYONE'S first project!) should be to make some blank files and do an empty theme with a couple of buttons, get them drawing correctly, resize them, get a feel for how it all hangs together. Once you've understood the basics, make a copy of the theme you're editing, make a new MCP layout, and then just statically place the elements where you want them. If you don't put any resizing logic in, it'll just go wrong if there's not enough space.
Shrug well if that's what you want
FWIW I suspect you'll find you don't really want to do any of this, because the results will be ...underwhelming. Could you explain more about what it is you want to achieve? Its possible there is some form of Reaper interaction you don't yet know about that might get it done for you.