We've sailed on the Black Prince 3 times although not to the destinations you're going to. However, clothing for evening meals shouldn't really differ wherever you're going! Generally, there will be at least one formal night but it depends on the length of your cruise. It's suggested that men wear a dinner jacket or suit and ladies a cocktail dress. However, I've worn a jacket and slacks before.
The rest of the nights will be a mixture of informal, casual, red,white & blue (british night) and possibly a western theme night. To be honest though just wear what you feel comfortable in - they're not going to through you overboard!
When you get your tickets it will tell you how many formal/theme nights there are.
Excursions from our experience tend to be very good, if a little expensive some times. Watch out for the rush out of the Neptune lounge when you're told to board your coach - some folk seem to lose their manners when it comes to getting 'their' seat.
Engine noise depends on where your cabin is. Certainly notice it in the Neptune lounge, Lido bar (chinking glasses and spirits bottles) but it's nothing to worry about.
The BP is a small ship so don't expect the facilities you get on the floating blocks of flats that are out there but it certainly packs a lot in for it's size and the crew are great.
Have a good cruise - I'm sure you will.