Checking my homework

[Christin]

Hello everyone,
could someone (a native english speaker ideally) check my english homework,please? I was supposed to write a short email to my friend asking for borrowing a bike.
My draft:

Dear Matt,

Could you please lend me your bike for a couple of days? My bike is broken and I and my family are going on a trip. We wanted to go by bike, but my bike is in a repair shop. We'll stay there only three days. I'd like to pick it up on Monday morning at your place because we are leaving on Tuesday.
Would it be possible?/ Can I count you in?
See you.
Christin

I'm not sure of using the tenses properly (highlighted sentences).

[Firefox]

Actually wanted or want work ok here.

Please: my family and I

[Christin]

Thanks for you help!
Why is "I and my family" wrong? (is necessary to hold the order)?

[Firefox]

It's not grammatically wrong. But in general it's more elegant to say "SOMETHING AND I" instead of "I AND SOMETHING". Putting the other person first is more a question of good manners than of good grammar

So, we have examples like:

My husband and I are happy to accept.
My sister and I went shopping.