Answer: Crows and finches will do several of the things you mentioned, especially uprooting seedings of corn and beans. Other possiblilities would be chipmunks and squirrels. Look for tracks, or if it is too dry, water the area and check for tracks the next morning.
Blooms on cucumbers and squashes only last a short time. Could you be seeing the natural drop of male blooms or unpollinated female bloom?
If crows or other birds are the culprit, your main weapons are scare tactics. Noise makers like a radio (check first with neighbors who might be bothered), mylar tape and balloons (the reflection bothers them), and strings down the row with streamers of flagging tape have all been used with some degree of success. Varying your scare tactics works best, as it keeps pests from getting used to them. Once seedlings are up about 8 inches tall, birds don't seem to bother them, so your distraction tactics need not last long. If scaring them doesn't work, you can get some bird netting to create a temporary barrier.
Q&A Library Searching Tips