re: Cherry table

Good job! This is a very nice piece.
Cherry is notoriously fussy. The stain will almost always come out blotchy, the best cure is sand it to at least 220, then a 50/50 mix of dewaxed shellac and denatured alcohol. This will seal the pores in the wood and make the stain a little lighter but the color will be even. As far as burn marks, Richforever has some great tips, but it sounds like your bit is dull. Take it to get sharpened or buy a new one. Don’t skimp on the bits! Buy the best ones you can find.