Well you are not going to like this but you did ask for advice, so here goes ...... I would return that kit if possible and start again with individual plants, larger pots and grow them outdoors if you can. Kits like that are a marketing triumph and the fancy pots are a classic example of style over substance. It's ironic it's called the 'gifted gardener' as you'd need to be one to meet the challenge of growing all those herbs indoors in that container. The pot is too small and doesn't make any allowance for the fact the herbs you mention have different growing requirements. On top of that thyme, oregano and chives are perennials. Parsley is a biennial and basil is an annual. The simplest thing to do would be to buy just a single growing plant of each herb (from a nursery, not the produce aisle) and see how you get on just keeping them alive inside. When you've cracked that challenge you can try your hand at growing from seed. But since you are unlikely to need more than one plant of oregano and thyme buying a plant is quicker and not much more expensive.

I pretty much agree with what floral_uk said.

I'd recommend starting with a couple of herbs in 8 inch planter pots. Oregano, Chives and Thyme will all thrive in a pot that size. If you must grow them indoors, they need to be in a very sunny location, like an unobstructed south facing window. That's not optional. None of the herbs you mentioned grow well under less than full sunlight for at least 6 to 8 hours a day.

Use good growing mix. For perennial herbs, a "bonsai" mix or a "cactus" or "citrus" mix works better (better drainage). Adding 1 part perlite to 3 parts "potting mix" works OK, too.

Clay pots work better for me than plastic. Don't bother with pebbles/rocks/marbles in the pots. Marbles in the saucer under the pot, to support the pot and keep it out of any water that drips through is actually a good idea.

Overwatering kills houseplants more than anything else. Water it when the top two inches of your mix is dry, not before that.

And fertilize herbs like this once every 4 weeks with a relatively balanced (3 numbers identical or very close to the same) fertilizer. Most "herb/vegetable/tomato" fertilizers are fine. Avoid "plant foods" with a high nitrogen content (first of the three numbers).

Also a note about parsley (and cilantro/coriander). Parsley and cilantro grow a deep tap root and need a pot at least 12 inches deep to rally thrive. You can put a total of 3 parsley and/or cilantro plants in a triangle formation in a 12 inch round planter pot (12 inches deep).

Good luck with it.

If you really must use that "kit," expect it to be disappointing.