your question could require a small book to answer. Depending on how bad the damage is, how badly the base wood is discolored would make a difference in what methods you may need to use to bring your table back to its former charm. Of course the total rehab would involve sanding the entire piece to bare wood and start from scratch. (see some of my previous answers on wood refinishing) If you simply want to do a varnish make over, you could use denatured alcohol to liquefy the existing varnish and remove/redistribute it. This can be fairly successful. Homer Formby made a mint selling kits that did just that. I have to say however, varnish is very old school and is rarely used today. It has tenancies to yellow, water spot easily and change color if a hot item is placed on it. Most high end furniture has a lacquer or urethane finish today. Lacquer is very hard to apply without good spray equipment is not an easy DIY project without some experience with that product. Urethane is easy to work with, comes in many finishes, satin to high gloss and can have color included. A fantastic durable finish can be created with several skillfully applied coats of urethane. Of course, if you chose to use urethane, all the old varnish must be removed and you would want to repair the wood base, restain or spot stain before refinishing with urethane or lacquer. The pour and forget kits you referred to are very gimmicky and rarely give good results. There is no substitute for good craftsmanship, and if something sounds too good to be true, it normally is. The only pour and leave product I have ever used with success is casting resin. This is actually a fiber glass epoxy resin that I have used on some commercial bars.
User is right saying you should cut the rough shape with a band saw. If you don't have one, you can use a jig saw but use the most rigid blade that will follow the form. The next step will be to use a table mounted rotary sander/ drum sander to work the piece to the scribed line. It will be next to impossible to make a well shaped piece without this step. Check out a few episodes of "New Yankee Workshop" online (PBS) to see the techniques. Keeping a full length of grain top to bottom is extremely important,(as mentioned) otherwise the piece will split in time. Good luck with your project.