a flat is an apartment. generally they're all on one level, unless its got a swanky mezzanine bedroom like in a loft apt, or when the building is split down the middle instead of by floors (not common, but i've seen it in converted houses- sometimes people buy a house, add more kitchens and bathrooms so there are both on every floor, then section off the hallways, and turn it into 2 or 3 flats, label them a and b for mail stuff- like 29 Acacia Road would become both: Flat A, 29 Acacia Road, and Flat B, 29 Acacia Road- and sell or rent one or all of them out to cover the mortgage + make a profit). flats can be above shops or in highrise buildings as well as in suburban/residential areas.
a 'studio flat' is a bachelor apt, which means you basically sleep, eat and watch tv all in the one room (bed might be in the couch, kitchen might be a nook sorta thing along one wall, or a small ajoining room) and you have your own bathroom.
a 'bedsit' is what it sounds like- you have a combined bedroom and sitting room (like in the studio/batchelor) but you have to share a bathroom AND kitchen with other people sharing the floor/building- like in university student accomodation. i think thats what you'd call a boarding room- they're rented rooms with shared communal facilities, and are considered lower class accomodation for poor people. a bedsit is the same set up as when you live at home with your parents really (you hang out and sleep in in your bedroom, all your stuff is there), only you have to buy your own food, cook it yourself in the kitchen, and chip in on the leccie bills if you haven't got sucktastic card metered or coin operated gas and electric, insteada your mum doing all the chores for you.
we don't have a lot of (or um... any?) condominiums in the UK as far as i'm aware (i'd never heard of them before i came to canada) but i spose a condo apt would be considered a flat too.