Glenn has a tutorial on cleaning and restoring the finish on cabinets in the tutorial section. You can see some repairs to veneer in my thread. It's titled something like "Singer model 27 Ella" also, I don't remember the name of it but J Miller has a good thread on a cabinet he restored with a lot of veneer work too.
If the veneer is loose it's just a matter of working glue under it and gluing it back down. Pieces that are missing can be patched. The patch will show but usually isn't too noticeable. If there's too much gone then sometimes it's better to peel it all up and replace it.
Your treadle cabinet looks like walnut from here. The other cabinet I can't see very well but there is a very good chance it's mahogany.
Rodney