bread cake and ice cream

Question

1) If you get a bagel or bread from a non-shomer shabbat Jewish bakery - what about a)the fact that challa isn't take off and b)baking is done on Shabbat? 2) Are pastry, cakes or waffles (fried flour or baked flour products) bishul akum or pat akum? 3)Is hard plain ice cream kosher? It may have glycerine, mona- and diglycerides? Thank you. Ketiva v'chatima tova.