If the fabric you use to line is plastic and solid (no perforations) then yes, you do need to supply drain holes. You cannot just "lightly water"......you need to water enough to satisfy the needs of the plants.

And the depth will depend on the type of herbs you are growing. Something like rosemary or even sage grow to be actual shrubs and are not well suited to a dish garden.

Yes. You absolutely must have drainage. What herbs are you going to use? Some are annual, some perennial. Some sprawl, some are shrubs. Are these intended for indoors or out? If indoors they'll need a huge amount of light.

I would also add that some herbs will require very different growing conditions, making them not very suitable housemates in the same container. For example, rosemary and sage like it very dry and very fast draining; oregano and thyme can take bit more moisture but not a lot and something like basil is a very thirsty plant requiring regular water. If you water enough to keep the basil happy, you will drown the others!