When the plants grow can I grab more seeds when they are grown?
As soon as your seeds sprout, you will get open pots and be able to get more seeds. Theoretically, you could have an unlimited number of sprouts, but only four seeds. In actuality, your sprouts will grow at the same rate as the seeds, unless you deliberately never water them.
(There was, as I recall, someone some years back who was experimenting with how many sprouts he/she could have at once before they would grow on their own, so the person never watered their sprouts. It got to be quite a large number, as I recall. I don't know if that person even plays anymore, but it was rather amusing to go to his/her garden and see all those sprouts!)
The one exception to the limit of four seeds is if you get a seed through the post pixie. If you already have four seeds, the post pixie seed will give you a fifth pot temporarily.