It is an internal happiness, for thatso she doesn't smile.

"For" meaning "because" sounds formal. With "for" it could be something like "It is an internal happiness; for that [reason] she doesn't smile."

She has a fashionable ear piercing in an ear and a cute cap in two colors.

I had forgotten, —she has beautiful socks, in two colors, too.

Using "em dash" instead of coma and avoiding the second comma are stylistic choices. Most punctuation guides recommend avoiding run-on sentences, that is independent clauses connected only with a comma.

This sheep itdoes not hasve any problems, and lovinges everyone equally.

It is a gladcalm and calmhappy sheep.

Repeating "happy" at the end is a nice closure.

It is an internal happiness, for thaHer happiness is internal; it doesn't need a smile.

Or.... It is an internal happiness, one that doesn't express itself in a smile

She has a fashion piercing in anone ear and a cute cap in two -colorsed cap.

I'd probably just say, "colorful cap" so it would be smoother

I hadalmost forgotten,: she has beautiful socks, inalso two -colors, tooed.

This sheep itdoes not hasve any problems, and. She lovinges everyone equally.

The two ideas are separate enough that I think separate sentences is more appropriate.

ItThis is a gladcalm and calmhappy sheep.

"calm and happy" is smoother but what you wrote is fine :-)