Is there internet on board?

Sometimes. If the mobile phone network is good enough it’s possible to access internet with a smartphone. The best way to achieve this is to buy an Indonesian SIM card for your smartphone (if it’s unlocked) and an internet data package. You can buy both in Padang before the trip, it’s not expensive. The best operator is SIMPATI/TELKOMSEL.
Do not expect the best coverage or data speed, though. Usually it’s enough to check and send e-mails, facebook and Messenger, check the swell forecast, and sometimes even to make video calls (skype, whatsapp, etc.).
But sometimes we can be out of coverage for a few days…