Yes, you can grow any plants and alchemical ingredients. The growth rate is inversely proportional to the value of the plant. Try to get a skill book that accelerates growth as soon as possible. Toward the end, you will be able to create an enchanted soil yourself. In the later stages of the game, plant growth will slow down (according to in-game rumors). To the first end of the game, you will probably have 8-10 unlocked cells.

thanks and this is such a cool system being implemented.

will I come across this fast growth book easily or is it more of a secret find?

This book is sold in a location directly north of the starting one.

inside the tower area does it unlock after some gems are returned to the mage statue?

The fastest way to get there is to buy an underwater weapon.

is this north of the starting area as in the wetlands?