Forward extension to extension on another PBX

One of your questions is easy, in this line

exten => 7051,n,Dial(PJSIP/555-555-5555@myVOIPprovider,,D(wwwwww705))

The variable ${EXTEN} is equal to the extension or ‘7051’, so you can use this or variations of it for substituting the dialed digits.

The CallerID issue I am not sure about, but you might have success using a dial string like this:

Dial(local/555-555-5555@outbound-allroutes)