No. If you put it through a strainer you will ntroduce oxygen and ruin your beer. Siphon the beer from above the trub and you will leave most of the unwanted stuff behind.
No need to strain if there is a lot of stuff floating around in it you can cold crash it for a few days and all that stuff will fall to the bottom of your fermenter.
nope, please don't do that . you just wait until the yeast and trub settles to the bottom, and you bottle the clear liquid above, and leave the trub at the bottom.
Best thing to do is siphon the fermented beer into a separate bottling bucket (with a spigot), leaving the trub behind. Then wait 20 minutes for remaining trub to settle. That will keep 99% of the trub out of your beer.