Firstly, leave it all alone. If you naff up wiring to the NTE's, then you will be liable for a hefty charge.
Why is the working socket connected to the other one using a yellow wire and a blue wire
The engineer has just extended the pair of wires as they were not long enough, sounds like they have used a bit of cab jumper wire, not a problem.
If it's the TalkTalk line that's not working, ring them and report it, don't fog the issue by telling them all about the engineers work, just tell them you have no dial tone, get them to arrange an engineer to fix it. When you see the engineer, then
tell him about what has happened.