~80% of Utricularias are terrestrial with flat leaves and traps that grow under the ground submersed in water (usually very wet soil). ex: graminifolia
~15% are aquatic and float with leaves that appear like strands or feathers. ex: vulgaris, inflata, radiata. These are EVIL in the aquarium.
~5% are epiphytes.
I suppose that since the terrestrial species are well adapted to periodic flooding and waterlogged soils (due to the need to keep their traps submersed) they would be capable of surviving fully submersed in an aquarium, or at least the majority of them.
Problem is finding the buggers! Usually you have to wait till they bloom (only for a few weeks in the spring) to find them. I saw one species in the field earlier this year but didn't think of taking a sample.
i think the extra plant they sent is U. Gibba. I'd estimate that each portion is about 2x2. I emailed them and they suggested 3 to 6 portions to start with for a 20gal tank. I'll try to take some pictures later.