Hello,
Are plants sentient beings? I mean, they do grow, they live , they grow old and die.
So, where do they fall in buddhism??

Thanks

The short answer is, that plants fall into the concept of the cycle of life, they are born and they live and finally they die-we are all subject to this fact you could also state that the relationship to a buddhist concept of dependent origination, this is where EVERYTHING is dependent on something else, e.g. for a plant to grow you first need a seed, the seed came from a tree that will or has died. So the new plant has depended on the death of another and so on.

They are not sentient beings in the full sense of the word, however they are living things.;)

Rebirth is not applicable to any living thing.

It's just transformation from one form to another.
If consider non-living this it just transformation of rock to sand and again sand to rock.

For living thing, it's a life cycle dependencies as explain by Xrayman.