I have a kitchen table with the shiny wood top, can I sand & paint?

If is wood for sure you can sand it, before you sand it would be easier to strip the shining surface. It's messy but results are amazing, then you have less sanding, just light sanding to give smoother feel of the wood.

Yes. Sand it then use a good primer followed by 2 to 4 coats of paint. Lightly sand between each coat.

I the wood is in nice condition, you may want to use a stain instead of painting.

Sand carefully, as it could be a veneer top.

Yes you can paint it

lightly sand and use a primer that is also like an adhesive to paint

you can ask for this at your paint store or large box stores I've done a table like this and had it several years with no problems

I did my entire dining set with chalk paint, and there's no sanding whatsoever, no need for primer. It just depends on the look you want. The top of my dining table was a shiny wood and I just wanted, after over 20 yrs., to have a different look. I finished the set with a low lustre varnish. A wax can also be used as the top coat, depending on the look one wants. The varnish and wax can be purchased in same brand as the chalk paint. I feel like I have a new dining set just for the cost of the product to paint and finish.