Having been going through this with my son the past few months, I'll tell you, it's NOT easy to get into that program!
1- Your pediatrician has to give you a referral (usually as an actual prescription), and you have to have your child's hearing screened by an ENT first, and your child needs to have a full developmental evaluation. My son did all this by 18 months (unless your child is Autistic, you're almost certain to have your application denied before 18 months since so much can change).
2- They send a single intake therapist out once all of step one is completed. This can take months (up to 3). The intake therapist evaluates the child in your home (the kids comfort zone), and 'scores' them. From there, the intake person has to clear the case with 2 superiors to see whether or not your child is eligible.
3- My son's insurance pays for it, thank goodness, because sessions out of pocket cost an average of $140 per HOUR.
4- Early Intervention only helps children up to age 3.
5- Yes, see number 1. You can get a second opinion with another doctor in the group if necessary.
6- Once therapy begins, they give you guidance as to how YOU can help. For example, per their instruction, I have to take my almost 2 year old to a preK class once a week once he's completely a month of speech and OT therapy (he's also getting services through the food clinic; his picky eating is relative to his speech delay).
7- Not that I can see as of yet!! :)
8- Yes, until age 3, then the records are turned over to you for safekeeping in case the issue continues into grade school; from there, you turn the records to your child's school.
My son is almost 2 and has the vocabulary of a 12 month old (when he was initially tested, he only had the vocab of a 10 month old). Because he's SO 'advanced' in his motor skills for his age, it kind of raises the bar, making his a severe speech delay. Sounds like your kiddo is right on track!! And as I mentioned, a LOT can change in a short period of time with little one's. Pediatricians don't tend to fuss over it until 15 months, then really get involved by 18 months.
You can help your son by reading to him daily, making sure older siblings aren't speaking for him, and trying to teach him sign language. The full developmental evaluation is huge; they dig really deep (like what your pregnancy was like!)... and they want to rule out Autism first (which is standard at 18 month check ups now).
PM me if you'd like more info, like I said, I've been living this for MONTHS :)