Last Saturday I have been the weenkend farm in Geoje.

⇒ Last Saturday, I went to a farm in Geoje.  (you cannot use have been because theere is a specific time reference which is Last Saturday)

Geoje city hall lent farm to the citizen for free.

⇒ Geoje City hall [or Geoje local government] lends farmlands to the citizens for free. 

My wife got a land to grow vegetables.

⇒ correct sentence

so I had to till the ground and sow seeds with my wife's mother.

⇒ That's why, I had to till the ground and sow seeds with my wife's mother. 

At first, Tilling the soil is interesting.

⇒ At first, Tilling the soil was interesting. 

But not much later, my back and finger began aching.

⇒ But not much later because my back and finger began aching. 

I regreted to come to the farm.

⇒ I regreted going to the farm. 

If my wife ask me to go to the weekend farm.

⇒ If my wife ask me to go the farm next weekend,

I should not go there.

⇒ I will refuse.

Hi Mr. Ryang Daehun! I'm happy to have shared some corrections to you. Please study the sentences well. Thank you.
 

♥ Teacher Liz ♥