If I'm not patient then I make a barbecue.

I agree with all of the corrections about the phrase "I make a barbecue". While it is true that barbecue is a style of cooking, and also the item used to cook the food, the phrase "I make a barbecue" can make sense in a different context. "I make a barbecue" could imply that someone is organizing an event where the primary purpose of the event is to enjoy barbecued food; however, this is not the case in this context.

I work from mMonday to fFriday, when there is somea holiday oin the week I prefer to rest at home with my family.

I make a different type of food, for example, jJapanese food and some dessert which is difficult to make.

If I'm not patient have no time then I make a barbecue.

I work from mMonday to fFriday, so when there is somea holiday onduring the week I prefer to rest at home with my family.

Days of the week should be capitalized.
The two clauses should be connected by a conjunction, like “so”

I make a different kinds of food, for example, jJapanese food and some dessert which is difficult to make.

“a different food” is singular, and in this sentence it makes more sense to say “different kinds of food” which refers to a variety of things.

If I'm not patient then I make a barbecue.

“make a barbecue” sounds odd, it is more natural to just say “barbecue”

“barbecue” is not really a noun that you make, it is more a style of cooking

I work from mMonday to fhrough Friday, w. When there is somea holiday onduring the week, I prefer to rest at home with my family.

The first letter of days of the week is always capitalized. To say you work "Monday to Friday" technically means you work Monday, Tuesday, Wednesday and Thursday, but not Friday (though if you say it like this most people will understand what you mean). Otherwise you could say "Monday through Friday" which includes Friday. We say "during the week" to indicate something that happens on a week day. Saying "on the week" is usually used to refer to a specific week. For example, "I will go to Aruba on the week of the 30th."

However, I don't stay at home doing nothingstill do things when I am at home.

Again, people will understand what you mean when you say this, but it is not technically correct. This sentence has a double negative: the words "don't" and "nothing" are both negative words, so when used together, they cancel each other out. To be grammatically correct, try using positive words instead, like "do."

I make a different food, fs. For example, jI make Japanese food and some dessert whichthat is difficult to make.

I think this is what you meant.

If I'm not patient, then I make a barbecue something.

"A barbecue" is the thing/machine that you cook the food on; it is a noun. "To barbecue something" means to cook something using a barbecue; here, "barbecue" is a verb. You could also say, "I cook something on the barbecue".