It's cloudy today in my area today. It's cloudy in my area today.

The original sentence is correct, but I feel it sounds a little better to place "today" at the end of the sentence in this case.

It's cloudy today in mythe area where I live. It's cloudy today in the area where I live.

Even without turning outff the heater, it isn't as cold as I think it is in my house. Even without turning off the heater, it isn't as cold as I think it is in my house.

Even without turning outff the heater, it isn't as cold as I think it is in my house. Even without turning off the heater, it isn't as cold as I think it is in my house.

Even without turning outn the heater, it isn't as cold as I thinkought in my house. Even without turning on the heater, it isn't as cold as I thought in my house.

Even without turning outn the heater, it isn't as cold as I thinkought in my house. Even without turning on the heater, it isn't as cold as I thought in my house.

Even without turning outn the heater, it isn't as cold as I thinkought in my house. Even without turning on the heater, it isn't as cold as I thought in my house.

Even without turning out the heater,MY GUESS: Inside my house it iwasn't as cold as I think in my house.uncomfortably cold, so I didn't turn on the heater. / 私の推測：家の中は不快なほど寒くなかったので、暖房をつけなかった。 MY GUESS: Inside my house it wasn't uncomfortably cold, so I didn't turn on the heater. / 私の推測：家の中は不快なほど寒くなかったので、暖房をつけなかった。

NOTE: I could not understand the original sentence. Remembering that much of Japan is now experiencing a "warm spell," I ventured a guess you did not use the heater. 注：元の文の意味が理解できませんでした。現在、日本の多くの地域で「暖気」が続いていることを思い出し、あなたが暖房を使わなかったのではないかと推測してみました。

I'm going to cook "teriyaki chicken" for dinner. I'm going to cook teriyaki chicken for dinner.

I'm going to cook "teriyaki chicken" for dinner tonight. I'm going to cook "teriyaki chicken" for dinner tonight.

NOTE: It sounds more natural if you add a time marker to the sentence. Hence, I added the word "tonight." 注：文に時間マーカーを加えるとより自然になります。そのため、「tonight」という単語を追加しました。

Even if I bought it, although it's very good, but it's a little expensive and the amount is small. Even if I bought it, although it's very good, it's a little expensive and the amount is small.

The 'although' shows that it is very good, but...

Even iIf I bought it, it'swhile it would be very good, but it's a little too expensive and the amount is small. If I bought it, while it would be very good, it's a little too expensive and the amount is small.

I also agree with Kallik's correction.

Even iIf I bought it, it's still very good, but it's a little expensive and the amount is smallre's not much in it. If I bought it, it's still very good, but it's a little expensive and there's not much in it.

Even if I boughtuy it, it's very good, but it's a little expensive and the amount is small. Even if I buy it, it's very good, but it's a little expensive and the amount is small.

Even if I bought it, it's very good, butWhile pre-cooked chicken from the store may be delicious, it's a little expensive and the amount isportions are small. While pre-cooked chicken from the store may be delicious, it's a little expensive and the portions are small.

From what I understand so far, in Japanese, a lot of the information can be assumed from the context without explicitly stating it. However, In English, it becomes ambiguous. In this case, it is not clear if you are referring to a raw chicken or pre-cooked chicken .

Even if I bought it, it'though the store-bought teriyaki is very good, but it's a little expensive and the amount (you get) is small. Even though the store-bought teriyaki is very good, it's a little expensive and the amount (you get) is small.

Another wording...

Even if I bought it, it's very good, but it'sMORE NATURALLY: The taste was excellent, but seemed a lbittle expensive and the amount is small.considering the small size. もっと自然に： 味は素晴らしかったが、サイズが小さいことを考えると少し高価に感じられた。 MORE NATURALLY: The taste was excellent, but seemed a bit expensive considering the small size. もっと自然に： 味は素晴らしかったが、サイズが小さいことを考えると少し高価に感じられた。

So, I have to go to the grocery store to buy chicken. So, I have to go to the grocery store to buy chicken.

So, I have to go to the grocery store to buy chicken. So, I have to go to the grocery store to buy chicken.

So, I have to go to the grocery store to buy chicken. So, I have to go to the grocery store to buy chicken.

So, I haveWell then... Mission Accepted! I'm going to the grocery store to buy chicken (instead). Well then... Mission Accepted! I'm going to the grocery store to buy chicken (instead).

So, I have to go to the grocery store to buy chicken. So, I have to go to the grocery store to buy chicken.

NOTE: The word "grocery store" has an image of a small local shop; in many parts of Japan (especially in big cities) "supermarkets" are more common. 　/ 注：「grocery store」という言葉には小さな地元のお店をイメージするものですが、日本の多くの地域（特に大都市）では「スーパーマーケット」の方が一般的です。