Linking to the app. During the tour, when you get to the GCH, they will give you physical tickets. You can scan these in to your disneyland app on your phone, and you will now be setup. it is highly recommended you do so, Jimmy mentioned some good reasons above. It is also a good idea to take a picture of the tickets on your phone, just in case.
You have to do dining reservations each day, unfortunately. There is no advantage given to hotel guests.
I don't think DL app really links your hotel stay unless you buy a package deal (hotel stay + tickets) from them, and even then it's rather limited. The
ABD is different, and thus your hotel is not in the app. the DL app is definitely missing some features.
So yes, you just book what you want in the app (or website). Please note that the following are difficult reservations to get, so you need to book them quickly (or get lucky later on): Blue Bayou, Trader Sam's, Oga's, Lamplight Lounge. Carthay Circle also can get booked quickly. The others you shouldn't need to rush as much.
You shouldn't buy
Genie+ except on the last day (after the good bye breakfast), or any additional post days, they are pretty generous with the lightning lanes. We didn't get extra Genie+ on this trip, and it was fine, but we had already seen most of what we wanted. Of course, if you really want to, you could get it on any of the days.