1.These are the chores that I usually do at home. First, I wash the dishes. Second, I make my dinner. Next, I clean my room. Then, I take out the garbage. And lastly, I fix my bed.

Daniel: (no heading)
Correct: These are the chores that I usually do at home.
Explanation: In constructing a paragraph, you have to make at least a sentence heading for you to start enumerating your activities.

Daniel: wash the dishes
Correct: I wash the dishes.
Explanation: Use the pronoun I to indicate the subject. In sentence construction, you have to have a subject plus the verb plus the predicate.

Daniel: Next, make dinner. Than, clean my room.
Correct: Second, I make my dinner. Next, I clean my room.
Explanation: Second and Next is called Transition devices wherein it indicates the connection of the statements. Since, you used the word "First" to start your paragraph, better to use "Second" before using "Next". Also, use the determiner "my" before the word dinner so that it will be emphasize.

Daniel: And, take out the garbage. Last, make the beds.
Correct: Then, I take out the garbage. And lastly, I fix my bed.
Explanation: And is used as a connector but in your paragraph, it is unnecessary to use. Since you end in the word "Next", it is better to use "Then" and And lastly". On the other hand, use pronoun I to complete your sentences.
Instead of using the word "make", it is better to use "fix".

2.I usually make dinner. I often take out the garbage. I sometimes wash the dishes and clean my room. I never fix the bed.

Daniel: I never make the beds.
Correct: Instead of using "make" better to use "fix" for better expression and better if "bed" is in singular form.