- You can't add halv- to all nouns, but to a few words it is possible! When you speak to a Swede you could try and see if they understand ;) For example circle (cirkel) and moon (måne) are possible words; "halvcirkel" and "halvmåne", respectively.
- Yes, it's countable. But in Sweden we don't count halvår! In plural it would be "halvåren" as "the years" would be "åren".
There are plenty of similarities between English and Swedish, especially when the English words aren't of Latin/French origin. The Old English version of year was "gear" (possibly pronounced /ɪea:r/ or /ɪeɑ:r/) and the Old Norse version was "jãra" (possibly pronounced /ɪea:ra/, /ɪa:ra/, /ɪeɑ:ra/ or /ɪɑ:ra/), so indeed these versions were very close. The Old Norse version eventually lost its initial /ɪ/ and became "ar", "aar" or "ār" (/ɑ:r/) in ancient Swedish (1250), which transformed into "år" in Old Swedish (1500).