Is it possible to call a number where you get asked to press 1,2 or 3 for a different menu etc. from a skype phone?
I have not had much success.

No idea on Skype, never used their software.

If you use a proper SIP based service though, you can select 'in band' on your DTMF settings either on the router, hardware phone or the software phone. That will do exactly what you're saying.