The mobile network coverage is quite good in the trekking regions where the infrastructure for tourism and transport is well developed. If you want to stay in touch while trekking in the mountains, it’s better to use CDMA phones and sim cards because the coverage area is much larger.
Internet is available on lodges and tea houses, but it can be a hit and miss affair. Your best bet might be to get a Nepali SIM card with a data plan.