Perhaps a phone call is a better way to sort this but I'll give it a try. If you want to get on the phone let me know, I'll rope in our business guy, between the two of us we got this.

Consultants come in two flavors, they can be just like employees but they get the crap work, or they are domain experts.

If you are going to be a 1099 "employee" you need to be aware that you are paying all the extras: social security, payroll tax, health insurance. I believe all the extras are about 30% but it varies based on your income.

Charging, I'd go time and materials almost every time. Stuff like this is hard to price, you just don't know how long it will take. So take whatever you think is a reasonable salary and I'd double it. Gutsy but see if they go for it. If you are good they will pay.

Good luck!