No problems at all. I went through various problems myself until I made it working.
I do not think that BK actually convert the geographical coordinates into UTM, I have tried it too. You need to do it manually with help of coordinate converter. There are many on google you can find. However you probably will need to use batch converter (well not point by point manually, but if you could upload whole file with coordinates and software will convert them all). I had many points to convert but I had problem to find batch converter, so I used below, but you might be lucky and get some free software to do it. Delft Dashboard can do it as well.
www.uwgb.edu/dutchs/usefuldata/utmconversions1.xls
I think GEBCO gives you bathymetry in lat and long so I suspect your problem is because tpxo files are using UTM then try to convert all coordinates into UTM and see if it is working.
In terms of TPXO file, no you do not need to extract your area, use whole files. TPXO files have data for extended area for example North Atlantic or another is just for Europe. Telemac extracts the points for your domain that is why you need to have match between TPXO coordinates and your case, so both need to be in UTM. Also I think you need fortran file as there is an option to use TPXO in the code. You do not need to change much there, just one option I think, the one I mentioned on my previous post.
Good luck!
Violeta