Most of the lodges along the circuit that advertised Internet actually did not offer it in the off season. An exception was the Tilicho Hotel in Manang, where you could use the owner’s laptop for 100 rupees. There may be other exceptions.
The first time I was able to use WIFI was in Jomsom, two weeks into the trek, at the Hotel Tilicho (a different one) near the a airport.
For charging my iPad, I never needed an adapter east of the pass, but west of the pass I usually needed it. In Kathmandu I usually did not need an adapter. Pokhara, I cannot remember.
The best way to stay in touch with people on the Annapurna circuit is by cell phone; they work in many or most places, certainly in most of the towns. Mine did not accept the local SIM card, so I paid Lal to use his.