Until when can we withdraw a resignation letter.

you can even do it on the 2nd last day as well according to previously known policy. but these are desperate times.

2 days before last day. Else becomes too chaotic

Can we take a sick leaves during the notice period?

A week or 2 before the LWD is the closest I am aware of. Hears rumours of till a day before lwd but no substantial evidence found of the claim.