I new to game and I have a question on farming.
There some land near my starting village between the mountain and the river I figure I could put some small farm plots on as they kind of small for anything else.. I was wondering if each plot will need its own farmer or can one farmer farm several small plots? Or is there a way to make irregular shaped farm fields.

Each farm field needs at least one farmer. One farmer can't tend many fields. Well, in theory you can try, by removing a worker on one field and putting him to the next, but it's not going to be very efficient and crops will freeze.

Crop fields can only be rectangular/square. You can't make a single crop field that consists of many small areas.

I tend to use medium sized or somewhat large crop fields, for instance 15x8 or 10x12, and put two farmers there. One may suffice, but will also often lead to some crop freezing when snow sets in.

There is a mod called Better fields that makes it a little easier to place crop fields (and orchards and animal pens), as the game becomes less sensitive to small indentations in the land. You can try out that if you wish. Using mods, any mods, will disable achievements, if you happen to care about that. You can't get new ones while using mods.

Ok thanks for the reply.
So the land between the river and mountain where I could make 4x3 and 3x3 plot of land is in fact useless terrain

It's not useless, but I probably wouldn't put crop fields there. They are too small. Doesn't sound like there is room for the odd house, but other than that you can put stockpiles there. I tend to put those here and there to fill out space.