Should be completely transparent
All standard finishes are transparent, but some are not without a little colour, or "water white" as it's usually referred to.
If you don't mind that it imparts a noticeable yellow/amber tone to the wood (which will increase slowly over time) then an oil-based polyurethane is a good choice here. This is the finish you can use that is toughest and most waterproof, as well as easiest to apply, for those who don't have access to spray equipment.
But if you'd prefer to keep the wood as close in colour to the way it is now then I'd go with a waterbased polyurethane finish. Waterbased polys are one of the classic water-white finishes and some are greatly improved over the versions available earlier one, when they were pretty meh.
Do note though that pine itself will darken slightly and go more yellow naturally with exposure to light, so the colour of the table will slowly alter over time.
Should be silky (as opposed to shiny - not sure what the exact term in English is)
You can say less glossy, or more matt (American: matte).
Semi-gloss, satin and matt/matte finishes are what you want as each of them is less than fully glossy. Sorry can't help with what each of those might be referred to in your language, even the direct translations of these words may not be of any help because the terminology is very varied*.
Shouldn't take a month to cure/dry
Both oil-based poly and waterbased polyurethane finishes take far longer than their drying time to fully cure. However that doesn't mean the table can't be used before then, just that the finish is not at maximum strength.
With oil-based polyurethane approximately a week to ten days after the last coat goes on the finish should be tough enough for light use, but baby it for the first month.
With waterbased polyurethane finishes as little as three or four days is enough to be able to use the surface, but it's still advisable to wait a week or longer before subjecting it to heavier use. With some versions it may take two full weeks for the finish to get as hard as it can get even if the drying time is less than a few hours.
The above are generalisations as all products are different. As well as that this is dependent on the conditions, primarily the temperature and humidity (the warmer and drier it is the faster a finish will cure usually). On top of that is coat thickness — obviously the thicker you apply a finish the more slowly it will dry and subsequently cure.
Resistant to heat/wetness/stains as it's gonna be a dining table
Good versions of both oil-based polyurethane varnish and waterbased polyurethane finish will provide the level of protection you're seeking.
Important to be aware that the total amount of any finish that you apply to the surface determines how resistant it ends up, most noticeably to scuffs/scratches and water penetration.
So even a very good version of poly won't provide high levels of protection if you only wipe on a few thin layers, but will give the level of protection that it's advertised to provide with three or more full-strength coats. I think personally that it is nearly always worth applying at least four coats for a dining table or similar surface.
*How shiny or not shiny a specific product is unfortunately varies because there is no standardisation across the industry. So regrettably you cannot assume that one company's version of Satin Polyurethane will give the same level of dullness as that of a competitor's product which you may have seen pictures of online.
In some cases there is a wide disparity, with one company's satin being close to gloss and another's being much more matt.