From the photos, hard to say if it's totaled. Rear end hits often can hide an awful lot of things. Shop will need to pull the bumper cover and pull back trunk carpet to get a really good look at the rear body panel and floor panel. If they're bent beyond anything really minor, I'd say the car is a total loss. Doesn't look like they hit you "square", rather tried to swerve to avoid and clipped the right rear. Did they impact the rim (do you see any damage on the tire or rim)? If there is suspension damage and unibody damage, then it's almost certainly a total.
As for how they value the car, the state usually has several approved methods. Most likely the insurance company will use a company called CCC, which is state approved. They're the big player in the valuation industry. It uses bunch of factors to value a car. Ask for a copy of the report, you're entitled to it...the should offer it to you up front. Make sure they have everything right. If the value is still incorrect, just be prepared to show them why. CCC is usually spot on with Accords, Camry, etc...but sometimes on an older car or more rare car, I find that they're not always 100% reflective of local market value. Sometimes it's low, and if the customer can show me why, I'll override it. Sometimes it's high, and in that case the customer winds up getting more than local market value(we won't adjust down...only up).
As for diminished value (DV), if the car isn't totaled, you'll need to request DV from the insurance company. There is already plenty of case law in the books regarding the ability to make a claim, but none that says it should be x or y amount. Every insurance company has their own methodology. I look at several factors, such as the cars age, mileage, severity of damage and pre accident value. Lastly, I'd check to see if the car was in an accident prior to this one (using the database that Carfax gets most of their data from). I don't know how many miles are on your car, but in all honesty, I'd probably not offer DV here. If I did, it would be a few hundred bucks tops.
Lastly, as for being paid for time off work. I'd be agreeable to paying for the date of the accident or maybe the day after. Beyond that, I wouldn't pay for time off work just for having to get an estimate, or make phone calls, etc... and the courts would not back you up on that either. Missing time due to injury is an entirely different matter, but due to inconvenience of an accident, no.
Hope this helps.