The panel that flips up is a place where one can put filters. The heat absorbing glass can be inserted there as well. Heat absorbing glass can be useful if you are using glassless carriers.
Subject to condition, the Componon is an excellent lens. It will work with 6 x 7, with the qualification that you might be limited in your enlargement size on the baseboard. I would guess that 11 x 14 might be the largest you can do, but others may correct me.
The Vivitar lens may very well be quite functional for 35mm and moderate enlargements. Use it until you get something better.
My reference indicates that you have a 35mm glassless carrier (#8053), a 6 cm x 6 cm glassless carrier (#8060), and a Universal Glass Carrier for all formats up to 6 cm x 9 cm (#8074). The latter should be fine for 6 cm x 7 cm (and other sizes) but if you would prefer a Glassless carrier for 6 cm x 7 cm I believe the part number is #8070.
I have a pdf format manual for the 23CIIXL. If you would like a copy, just pm your email address to me.