If you remove plants, they should respawn in the same spot. In order to grow them in your Sim's garden, you need to wait until they put out fruit or flowers. At that point, the "harvest" option will show up. Then you can plant the fruit or flowers. If your Sim has Level 5 gardening skill, you can take a cutting from a wild plant and graft it onto a plant on your Sim's lot. This is very useful for slower growing plants. That said, grafting appears to be broken at the moment, so you would have to wait for the plants to become harvestable or buy seed packets until that is fixed. If you fish in the pond in Sylvan Glade, you can catch pomegranates.
In order to graft plants to get cowplant berries, you would need to graft strawberry with snapdragon to get dragonfruit. Plant dragonfruit, then graft the dragonfruit to the snapdragon. You would still have to harvest and plant the berries to get a cowplant. You can also catch dragonfruit while fishing in the stream all the way in the back of Magnolia Blossom Park and some other places that escape me at the moment--maybe off the pier in Magnolia Promenade.
I should add that the plants only grow when your Sim is actually on the lot, so if you go home and wait a day or two to go back, the plants won't have grown. They will be just as you left them.
