1. will stay
We will stay at home.
>This sentence is correct.

2. looking
I am looking at the big ballon.
> I am looking at the big balloon. 
> Be careful with your spelling. 

3. will go
We will go to a science museum.
> This sentence is correct. 

4. running
I am runnig because I'm too late for school.
> I am running because I'm too late for school.
> Be careful with your spelling. 


5. caught
I caught a dragonfly in fall.
> This sentence is correct.

6. bought
My mom bought the toy to me and my brother, Ryan.
> My mom bought a toy for me and for my brother, Ryan.
    or
> My mom bought a toy for us.
> My mom bought a toy for me and Ryan.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Usage of "for and to".

 They are both  prepositions but they have different usage in a sentence.

~In your sentence we need to use "for" because your mom intended to give the toy for both of you. 

*For is intended to give
*To is receiving.

Example:
 
~ I lent my bike to my brother.
~ I will buy this hat for my brother.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Thank you for doing your homework, Eric. ^^

        You have only few corrections. Keep it up! Kindly take note as well the corrections I made for you. See you next week.

      Have a great weekend.

~Teacher Cassie