Hi crazifox, The plant goes by the name of Tradescantia (commelinacae) not sure about the variety as there are lots. What I do know is that it looks like the type commonly grown as a houseplant (T zebrina) They come from Mexico, so not hardy outside (in UK) the common name is 'wandering jew'. It grows incredibly easily from cuttings and needs regularly pinching to keep it bushy. Its a trailing plant grown mainly for its foliage but as yours has, it does flower. Water and feed well in summer and keep relatively dry in winter.
Regarding the 'white fluff' on the leaves, I expect its a pest called 'woolly aphid' and it lives within the fluff feeding on the leaves. To control it, use any general systemic aphicide and repeat at 14 day intervals until its gone.
regards, Lannerman.