I have a Japanese maple tree, about 20 ft.
I pruned few branches in the winter and now I see many branches didn't grow leaves. When I touch it, I can tell some branches are dry easily as they easily break. However some of them seem flexible and also have tiny triangular branches that could have been leaves?!
My questions are:
How can I tell if a branch is dead and need to be cut off.
Second, when is a good time to cut dead branches?

One example photo attached.

You have already figured it out: flexible branches aren't dead but brittle branches are. You need a pruning hook. If you have a long handled pruning saw or long handled pruners, you may already have one. Hook the hook over a branch and give a sudden jerk. The dead branches will snap off easily but the live ones will bend without breaking.