Bitcoins values are stored in 64-bit integers, with 1 BTC stored as 100,000,000 which gives plenty of room to fractionalize, since it's stored as if it where a double-precision number.

Integers. BTC is only used for display; everything is actually computed in terms of Satoshis (1 BTC = 10^8 Satoshis). Thus very small transactions are possible.

Bitcoin transactions can go down to 0.00000001 BTC. They aren't however stored as floats due to rounding errors this can introduce (https://bitcointalk.org/index.php?topic=13837.0).

Floats. You can pay with any fraction of a Bitcoin AFAIK.