How well can your vocal range be improved with lessons? & How do I find a good teacher? I know I can sing, but I have breathing problems and problems following the notes, I'm into to singing big songs, I just wanna learn how to do it right
Hi "I just want an answer":
You have multiple questions and topics – so this reply will have multiple answers. 
I'm going to assume a couple of things: 1) that you may still be in your teens, and 2) that when you say "improve" you mean expand to a larger range.
If you are a teenager – even in your late teens, your voice range is in the process of developing . . . and it takes some years for it to settle. Yes, with a good teacher and enough time you should see your range expand ("improve"). Daily practice and good habits will enable your voice to develop well. Your limited range will grow to something resembling two useful octaves … and maybe more.
A good teacher will instruct you regarding your "breathing problems".
A voice teacher is not responsible to teach you how to read music. For that you'd do well to study an instrument (like the piano) and start a systematic regimen of sight-singing exercises every day. Inability to "follow the notes" is a musical problem that you can remedy in this way.
There are a couple ways to find a good voice teacher. One is to ask your friends and teachers for referrals to reputable local voice teachers. If you get the chance, ask your prospective teacher for permission to "audit" someone else's voice lesson, so that you can watch, listen and gauge whether you would get along with that particular teacher. Another source is to go to the following web site and do a search for NATS members (voice teachers in association with National Associate of Teachers of Singing) in your area. Names and contact information should be readily available.
http://www.nats.org/find_teacher.php
I hope this has been helpful.