If I put Boots (which permanently add 2 movement spaces to a Unit) in the inventory of someone in my StreetPass party, and then StreetPass with another Fire Emblem player, can that other player then buy the Boots from my party?
No. Here is a link that has a table of items that are not available for sale via StreetPass teams.
Sword Missiletainn, Sol, Amatsu, Falchion, Exalted Falchion, Parallel Falchion, Mercurius, Tyrfing, Balmung, Mystletainn, Sol Katti, Ragnell
Lance Luna, Gradivus, Gáe Bolg, Gungnir
Axe Vengeance, Wolf Berg, Hauteclere, Helswath, Armads
Bow Astra, Parthia, Yewfelle, Nidhogg, Double Bow
Tome Valflame, Mjölnir, Excalibur, Forseti, Book of Naga, Goetia
Staff Goddess Staff
Item Naga's Tear, Boots, Bullion (S), Bullion (M), Bullion (L), Supreme Emblem
DLC Dread Scroll, Wedding Bouquet, All Stats +2, Paragon, Iote's Shield, Limit Break, Silver Card, Outrealm Item