so if The Doctors memory has been wiped of Clara, then how will he remember his regen from 11 to 12 or his various adventures with Clara? has he forgot all those adventures?

no, he said in the diner that he rememebred the ice warrior siege etc, but not anything about what clara looked like or was. only bits of detail

She has been removed from his memories. Everything about her. Nothing else, just her. He knows he was with someone, but doesn't know who she is.

No, he remembers the adventures, but not Clara. He knows she was there and the things she said and did, but he can't physically picture her.

Unless that changed when he saw the graffiti on the Tardis.

Even then, he'll know what she looks like, but nothing about her personality (other than what he remembers from the conversation in the Diner)

Does his narration to waitress Clara include his post memory-wipe self knowing why the memory-wipe was necessary? Otherwise he could presumably go back and observe any number of events from Clara's life whilst hiding behind lamposts and wearing false moustaches.....does he know enough not to go pulling on that thread.

Personally, I think it was the emotional intensity and need of the Doctor for Clara that was erased. If it was a "simple" memory erase, there would be a thread and he would go "pulling on it".

If it was just his memory of Clara that had been erased, just how long do you think it would it take for him to notice there are holes in his memory? Not long. And the one thing the Doctor can't resist is a mystery. Therefore, it can't be a straightforward memory removal.