Right now, I'm not in school because of an illness, so I'm on a large break.

Could also split it up into two sentences. 'Right now, I'm not in school because of an illness. So, I'm on a large break."

I spend my day doing my hobbies, and I help with the chores.

Could also say 'I spend my day doing my hobbies and helping with the chores.' Your preference.

In general, I try to improve on my daily tasks.

This is a bit awkward.

Right now I'm not in school because of an illness so I'm on a largeong break.

I spend my day doing my hobbies and I help with the chores.

The fact that they’re your hobbies is implied, no need the possessive noun ‘my’.

In general, I try to improve on my daily tasks.

Generally, I try to get a little better in my tasks every day. <<<< more natural

Right now I'm not in school because of an illness, so I'm on a large break.

You can also say "a long break," or "I am taking time off."

I spend my day doing my hobbies and I helping out with the chores.