Do tzitzit need to dangle? Can one use some velcro to pin the strings down along the side of the beged so that they don't dangle down and get in the way of things?
No, they do not need to dangle. Many rabbis, including my Rosh Yeshiva, tuck their tzitzit under their belt to keep them neat and prevent them from ripping on nearby objects. In addition, letting them dangle could be considered "undignified" and "shlumpy." Rabbi Menachem Posner of Chabad recommends "tucking them under your belt and then into your pants pockets. This way, they are still visible, but stay neat and tidy."
Of course there are plenty of opinions that allow you to tuck tzitzit into your pants, but it is not universally accepted. In Az Nidberu, HaRav Zilber zt"l wrote a very forceful tshuva saying you cannot tuck tzitzit in, and those who cite the Arizal misunderstood him!
I doubt that tzitzit have to dangle, but it seems to me they should. I vaguely recall a halacha regarding tangled tzitzit (the Gra is machmir on this) being problematic and the terminology of tzitzit tying -- the knotted section is called the gid and the rest is called the anaf -- seems to imply the tzitzit should dangle.