My cCats in the sSummer

This is okay, too. We capitalize the first letter of important words in titles.

These are okay, too:

My Cats in Summer
My Cats during the Summer

On one hand, ite is Molly, a black female cat thatwho is 12 years old, allegedly, because she is tiny and skinny and she has a lot of energy when she plays.

On tThe other hand, is Mickey, a mixture of sSiamese cat and another breed that resulted in a quiet and loving cat who is the perfect yang for Molly.

They don't really look worryied about the summer heat because you can see them ion the balcony enjoying the morning sun or having a relaxing siesta during the warmest hours.

However, tThey usually drink a lot of water, however, and layie down on the refreshcooling mat when they are overheated.

lie, lay, lain　→ intransitive, takes no direct object
lay, lay, laid → transitive, takes a direct object

Strictly speaking, we're not supposed to use, "however," at the beginning of a sentence but a lot of native English speakers do.

On one hand, itThere is Molly, a black female cat that is 12 years old, allegedly, because she is tiny and, skinny and she has a lot of energy when she plays.

It's generally not considered good English to list like " A and B and C ", we'd rather use " A, B, and C "

On the other hand, isThere is also Mickey, a mixture of sSiamese cat and another breed that resulted in a quiet and loving cat who is the perfect yang for Molly.

I like the use of the ying and yang expression, but I think usually we would say it as "X's ying to Y's yang", i.e. "who is the perfect ying to Molly's yang." But your's works as well!

They don't really look worryied about the summer heat because you can often see them in the balcony enjoying the morning sun or having a relaxing siesta during the warmest hours.

However, they usually drink a lot of water and lay down on the refreshingcool mat when they ( are heated/ feel ) hot.

I think refreshing has a slightly different nuance (I would say water is more 'refreshing' than a mat for example)

My cCats in the summer

You could say “my cats during summer” however you mostly talk about your cats specifically; as they are for majority of the text, so this makes more sense :)! And is more natural

On one hand, it is Molly, a black female cat that ise is a black cat named Molly. She is allegedly 12 years old, allegedly, because she is tiny and, skinny and she has a lot of energy when she plays. However, I do not know her exact age.

We usually say: “allegedly” + fact/event/speculation ! Since the speculation is her age, it is best to say your sentence in this word order !

If you are doing adjective + adjective + adjective, only ever use ‘and’ to connect the last two: for example as I put it:

“She is skinny, playful and sweet.” Is correct
“She is skinny and playful and sweet” is incorrect !

Of course I understood everything you said perfectly, this is just how natives would put it :)

On the other hand, there is Mickey, a mixture of siamese cat and another breed that resulted in awho is has a very quiet and loving cat whopersonality, thus is the perfect yang for Molly. He is also a mixture of Siamese and another breed.

‘On the other hand’ implies a contradictory statement which is about to approach. As you’ve just mentioned Molly’s personality, it would be best to say his qualities first.

We wouldn’t naturally say “he is Australian resulting in his vigilance” or frame qualities ‘as a result’ of a race, it is better to say it as a part of his personality as I have done above!

TheyI don'’t really lookthink they usually worry about the summer heat, because you canI always see them ion the balcony enjoying the morning sun or having a relaxing siesta during the warmest hours.

I changed this to your first-person perspective ‘I’ as you are stating an opinion !

We would say ‘on’ the balcony, like ‘on’ the beach, field etc!

However, they do usually drink a lot of water and lay down on the refreshing mat when they are heatedmat to cool down.

We wouldn’t usually attribute ‘refreshing’ to an inanimate object, unless it’s like a drink or song or music etc. unless the mat is cold, but I am not sure if you meant to imply this!

“To cool down” -> to alleviate heat by going inside, bath etc!