Pedals are important because the serve as the contact point between the rider and the bike’s transmission. Clip-less pedals systems come in a variety of designs favoured by individual manufacturers, but the mechanics of all styles are roughly the same. Tiny adjustments in the position of the show cleat – that snaps into position on the pedal – can make a big difference to the comfort and health of the rider.
Yes, bicycle shops generally provide repair services. A typical list of offered services includes regular service/adjustment (including safety check; and brake, drivetrain, and tire inspection); premium, and annual service, which is a more extensive tune-up. More specific repairs include drivetrain tune-up, brake system tune-up, flat tire fixes, brake repairs, cleaning and touching up the bike frame.
Modern bottom brackets use a sealed bearing type construction that keeps water and debris locked out, so they seldom go wrong. Maintenance is impossible so they need replacing when they do wear out. Older style cup bottom brackets need to be re-greased every now and again, and occasionally will need to have their bearings replaced. There are a lot more teeth on the chainring cogs than those on the rear cassette, so need changing less regularly. Cranks usually a solid one piece construction so there is not much to go wrong.