I have tried importing .tpe files, and get errors relating to difficulty with some floating point numbers.
.tpe support is pretty new and there hasn't been much exposure yet. Please open a bug for this on the website and attach the .tpe files you're trying to import.
I have tried with .csv files made with excel and get errors saying there are no channels.
CSV is an encoding, not a file format, which means you can't just save anything as a .csv file and expect chirp to be able to read it. Download from the radio, export to CSV, then edit that in your spreadsheet, and import the result back into chirp.
I have even made changes to the data in an .imgfile (XML), and get told it's an invalid format.
An image file is not an XML file, and if you have XML data in a .img, then that's potentially part of the problem. However, you shouldn't be editing XML by hand as you're very likely to break the very strict formatting.
I assume all of this is because you don't want to use CHIRP's integrated memory editor for some reason? That surely seems easier than hand-editing XML files :)
Also I am not sure that I really understand what all the columns are in the main display.
You'll need to ask specific questions here as most people find them fairly self-explanatory.
And is there any documentation available? I sure can't find any.
There is a little. Feel free to write some :)
The FAQ and beginner's guide on the main page are the bulk of what we have right now.