Here's a brief overview of sponsors, answer is in there somewhere. Forum is rarely visited unfortunately, everyones on the chat and responses to FAQs get lost as we go, hence the Wall of Text.
1) 'Progress' is a holdover from a prior regime, there is no progress. You seek terms the sponsor will accept and they will charge you points, you input the points demanded in the commercial points box of the offer sheet and once you have sufficient points stored to cover it, the sponsor will be automatically signed.
Edit:- I forgot something Major. Cooldown points. On top of the points demanded, an amount of points is added onto the demand to allow other teams a chance to sign the sponsor. This points requirement will expire over time.
The way the system works currently is if a sponsor wants 350points and you offer 1000, as soon as you have 350 they will sign(I've no idea what would happen if you actually had 1000 points). If the cooldown points are a further 300, they will sign at 650. If you offer 350 they will not autosign until cooldown expires.
2) Sponsors will only negotiate with you if there's a green tick on the main screen for your division.
3) If you've no sponsors you can sign AVAILABLE NOW sponsors but if you already have a sponsor you may not sign a pre-contract with these guys. (The season start will always conflict, preventing a deal.
4) Once you open negotiations, top of the screen you'll find interest level in a text box titled negotiations. Some if not all sponsors will refuse to negotiate without a minimum interest level, typically 4 or 5/10. Interest is aquired by your start of season presentation which affects all suppliers to an extent and subsequently through investing points in individual sponsors. Interest is raised by selecting increase in the increase interest box on the right.
5) If you're getting a response in red lettering "offer to low", it'll be because they don't have sufficient interest, you're division is too low, you've a poor quality Commercial Manager or the terms are excessive. Ultimately, if you've maxed interest you can't improve your position, so you need to reduce the terms to strike a deal; less money, less missed races, shorter term length.
6) There is one pool of sponsors, which while large sees quite a bit of competition. Other teams are competing with you for their sponsorship. You can see how many teams are negotiating under progess, the max number of teams the sponsor will sign under sponsor information, and the state of play on the main screen i.e. 1/2 means, one team already contracted one deal available.
Just because a team is listed as negotiating doesn't mean they are. You can't see starting terms until you open up negotiations and pulling back costs you interest. A lot of guys will open up multiple sponsors and negotiate with one, leaving the others as fall backs if things fall through.
7) Power position, as teams open up negotiations with a sponsor their power position rises due to demand. It'll cost you more points to get the same deal as PP rises. Factors that affect it include competition from other teams, your division, whether or not their available now, their wealth level, their negotiability, your staff quality, etc.
8) Teams can only store 1000 to 1300(from HQ) points meaning you can't sign a sponsor who demands more than 1000 points, if you're willing to risk being gazumped you can set a deal where the sponsor demands more than 1000 but 'invest' points in the deal to bring it down under 1000 and keep the good terms. The problem is that points invested are lost if you don't get the deal done.
Hope this helps