How to write a good private school admission essay(s). To brag about myself?

I'm applying for a couple of private schools and i need help in making my short answers/essays sound...good. They have to be interesting and catch the reader's attention but can't be too..."crazy".

What do you like about yourself? Why? (word limit 150)

--> i shouldn't brag about myself here.
--> the "WHY?" part is the hardest to write about.
--> if i said, "i like how i'm determined." how are you supposed to say why? determination is obviously a positive thing. what else can you say about that?

--> should i say i'm stubborn instead? but that's...a negative definition of determination.

well, it starts here:

(i feel like i need an intro but...idk what to put) I like how I am very determined. If I needed to turn in an essay for school the next day, I'm determined to finish writing it. If I needed to run a mile under eight minutes, I'm determined to practice until I have reached my goal. If I needed to play three hours of tennis in the scorching sun, I'm determined to endure it and not take a break. Determination is the quality of being resolute or continue trying to do or achieve something that is difficult (this sentence needs to be revised. xD it doesn't make any sense...OTL maybe it's the verb tense?). With determination, I can do anything (this feels cliche).

and...the second one:

Imagine you are a (the school's name) student and you invite a fellow classmate--who is from a very different part of the world--to join you in your hometown during a school break. What would you feel would be important to share with him/her during his/her short stay and why?

--> i feel totally lost on this one and i don't know what to write.
--> they would um...miss HOME.
--> i would make them feel at HOME. uh...but i don't know where they came from...O_O
--> i would share with them the culture of my hometown.
--> have fun.

OTL please help me.

I would start by getting rid of most of the determined's. Show off some vocabulary or just go to thesaurus.
The 150 word limit is tough, but i would still try to give an example of a time when you were determined instead of saying what you would do "if" you were in those situations.

For the second question talk about what is special about your town. What would you like to share with someone. Maybe something that they wouldn't have in their country or something that is unique to your city.

Hi Julie, you can do this without bragging. Focus on your interest. Want to know what I like about myself? I am good at explaining things; I like that about myself because I feel a calling toward education as my field. I have a very bad sense of direction (and style, for that matter), but I am so glad that I am good at explaining things because what is most meaningful to me is the ability to help other people understand stuff.

So answer that question by sharing your aspirations and values with the reader.

Do not just say a general concept, like determined or stubborn. Put it in the context of your academic/professional plan.

For the second question... that is a tough one! I like to always suggest that in any essay you should let the ideas reflect the plan you have, your serious plan that is so meaningful and important to you. How can your plan be reflected in the way you accommodate a guest? :-) Depends what your plan is...