Is hitting the Hoshanos on the ground a universal practice? And what is the source for this custom?
The source is the Gemara, Sukkah 43b-44b, which calls this practice מנהג נביאים (a custom instituted by the prophets) or יסוד נביאים (a practice established by them). (The Gemara ends up ruling that the first version is correct, and that therefore we don't say a berachah for it.)
On 43b and 44b the Gemara mentions, in this connection, חיבוט of the aravah. (The following mishnah, on 45a, also mentions the opinion of R. Yochanan ben Berokah that in the Beis Hamikdash, they would חובטין palm branches - rather than aravos - on Hoshana Rabbah.) Rashi on 44b (ד"ה חביט) understands this to mean "waving," but Rambam (Hil. Lulav 7:22) says that it means "beating," and says that it can be done "on the ground or on a utensil"; Rema (Orach Chaim 664:4), citing Tur, says that we do both - first wave it and then beat it.
Kabbalistically, it should be beaten specifically on the ground (Zohar 3:32a). Mishnah Berurah (664:19) compromises: first beat it on the ground (five times, in keeping with a statement by Arizal), then continue beating it on a utensil to knock off the leaves.
Reasons behind this practice: Taamei Haminhagim cites Tolaas Yaakov that it is "to destroy the [severe] judgement so that it not be found, and bring it down to the dust so that it ceases to exist from the world." (In Kabbalistic writings they speak of the "five severities," which is why Arizal says to use five aravah branches and to beat them five times.) In a footnote there he also cites Levush, that it is done as an expression of joy.