Less, paskening according to Kabbala is a big discussion. As for your rabbit’s foot, it is definitely darchei Emori (a goyish superstition probably based in avoda zara). It certainly wasn’t lucky for the rabbit. Breathing has a logical reason. Therefor it is permissible. However, in general during davening one should stand as one would in front of a king or important official. Rav Moshe and Rav Soloveichik both stood stock still. Perhaps a soldier in the US Army should stand at parade rest (in fact, I have noticed that many frum men walk with their hands folded on their backs).
As for the OP’s question, Rav Eli Mansour says “The Halachic authorities rule that whistling was not included at all in the decree against producing sounds on Shabbat, and one may thus whistle a tune on Shabbat. We should note that irrespective of the laws of Shabbat, whistling in public, such as while walking in the street, is improper and unbecoming of a Torah Jew. But if at home one wishes to whistle as background to the singing of Pizmonim (hymns) at the Shabbat table, this is certainly acceptable and permissible.” Of course, if one has a guest who is annoyed by whistling and wants him to continue coming around one should refrain. It is simply a good midda.