Teak dining table - how to make it smooth  

Because the top is solid teak, it is going to move (expand and contract) as the ambient humidity changes.  This is why those cracks are there.  They occured when the wood shrunk at different rates as it was drying causing significant tension across the grain, and consequent cracking.  As such the cracks are going to be the primary places were you will see this wood movement manifest.  
So, if you were to put a solid filler in the cracks you would see it crack as the cracks intermittently opens more, and/or you would see it crush the filler and push it out.  
I am not sure there is a flexible gap filler that would accomplish what you are looking to accomplish.
Generally this sort of "character" lower grade (this is not a derogatory, simply how a wood worker would describe a slab with checks and knots and such, and in fact such a slab might occasionally be prized above a straight grained slab) slab table top is appreciated for its natural characteristics.  
The same sort of principle applies to the general flatness of the top.  If you have it flattened, you very well may discover that it expands and contracts up and down in certain areas such that it is no longer flat.
If it were mine I would oil it and appreciate it as is.

Thanks for your quick response.  My worry is also about food particles and what not getting in the cracks.  Any suggestions or just use place mats and be careful?
Also, what oil do you recommend?  Tung / linseed / teak?  What about beeswax?  Or perhaps more than one (if so, in what order)?

First, a massive slab of solid wood like the top of your table is not what would normally be described as "dimensionally stable" no matter the species. Wood moves in accordance with relative humidity and temperature of its environment and varied, swirling grain just complicates the internal stresses seasonal movement will exert. That said, the best you can do would be to provide a stable environment for your table. Depending on variables like age and environment, expect a certain amount of variation with regard to flatness of the surface. This is completely normal, natural, and part of the charm, IMO.
Personally, I would want to celebrate the unique qualities of the material. The voids should be left as is. There's no effective long-lasting method of filling them that wouldn't call unwanted attention to them anyway.
You are lucky to have an unusually large piece of solid wood furniture in your home. Really, beyond regular cleaning and a periodic sanding, re-oiling, and/or paste-waxing, I wouldn't do anything at all except enjoy it if it were mine.

Agreed with tktoo. It's gorgeous as it is. Beeswax or oil is fine, but I wouldn't put anything permanent on there.
If you are really worried about food particles, though--and I have a little kid, so I certainly know how that goes--have a glass top made that overhangs the wooden slab by a few inches. Use a few clear silicone buttons on the bottom of the glass, so it'll stand off the wood and won't rock. You get to enjoy the look of the slab but the dining surface will be sanitary, and you can take it off anytime the mood strikes you.

I agree with @tktoo and @toomanychairs as well.  I really like the combo of 100% tung oil followed by beeswax.  It gives a really nice semi-gloss finish, some extra protection, and is easy to maintain.  Apply and rub the beeswax with #0000 steel wool and enjoy.  And as @toomanychairs pointed out, you can always get a glass top for it.

I think oiling is the best option that you can prefer. The wooden piece you bought is beautiful and oiling will give it a glossy finishing. I too had wood dining but recently I have replaced it with granite top as it is easy to maintain.