If you build a tent it’s boneh, unambiguously one of the 39. I don’t see why umbrellas are in question. They’re either assur because they’re comparable to ohel, or because so many people hold they’re comparable to ohel that you assur them for another reason like “zilzul shabbos” even though you don’t think they’re ohel.
Bikes are assur. I don’t fully understand why, but I agree with DY that a “no” is a more appropriate answer than “ask your LOR.”