Can we place silkscreen inside the footprint for through hole PCB? I guess it eliminates "visual congestion". What are the problems associated with it??
You can put silkscreen markings anywhere you want on a board. There is nothing special about being "inside" a footprint of a particular part. It is quite common to put markings inside the board area of a part. Just keep in mind that these will be covered up when the part is installed, so such marking are only of use during assembly or when looking at a bare board.
Silkscreen should never cover pads, but every board house I have used automatically clips the silkscreen layer to only where there is soldermask. It's not good to rely on this since registration may not be as tight as the clipping. Don't do it yourself, which leaves the board house clipping as a extra layer of protection against screwups.
Yes you can and I've done it many times. I guess the only problem associated with it is the obvious that you won't be able to read the designators once components are placed over the top, so maybe consider that for connectors and other items where you'd still like them to be visible after the board is populated.