We have not been on the infinity but have cruised Celebrity since 1992.
There are not a lot of activities poolside. The band does play for about an hour around noon. Otherwise there is canned music. On some Celebrity cruises, there was maybe one afternoon where there was water games, and another where there was drink mixing demo. There really isn't a whole lot going on poolside. We cruise Celebrity for their laid back atmosphere - it is truly a restful and relaxing cruise. There are activities that go on - but they are not in your face.
The announcements are kept to a minimum - once a day around noon, the captain gives the temp, location, speed, etc., and the cruise director will announce the activities (the only time activities are announced). Any other announcements are regarding wildlife sightings (dolphins, whales, etc), or informational (ship is cleared so you can proceed ashore).
From what I have heard from others who have cruised different lines is that Celebrity is among the most formal of the mass market lines. The dress code is to be observed in public areas in the evening (except for the casual dining boulevard - pool deck). We have seen people turned away from the show because they changed after dinner.
The food is very good with everything made on board with the exception of the sugar free ice cream.