It sounds like some people misunderstood your 4-hour date description. I doubt anyone would sit in a restaurant for 4 hours... That's absurd. I'm sure what she means (and you wrote) is that the date will last for 4 hours, including dinner and private time too. 80% of my first dates are dinner or cocktail dates, and yes, they start in a public place. Women choose to do that for various reasons, in your case she seems to use the dinner portion of the date as additional screening time, and I'm sure she feels much safer meeting you in a restaurant than in public, which is reasonable, considering your lack of references.
On my dates, I always receive the donation in an envelope or gift bag within 10 minutes of meeting. Sometimes it says "Happy Birthday" or my name or "Thanks!" on the outside of the envelope. I prefer to get the donation out of the way, so I can spend the rest of the date relaxed, without having to think about the "business" part of the equation. After sharing some drinks or a nice meal, we head back to my hotel, and sometimes I choose to drive, sometimes we catch a cab. Generally on a cocktail date we will spend an hour having drinks and another 2-3 hours in private. On a dinner date, dinner will take 1-2 hours, and we spend another 3-4 hours in private. I'm sure your dinner date will be similar: perhaps 1-2 hours in public, then you will head back to her place 2-3 more hours of fun.
A few bits of advice:
- This is common sense, but dress for the occasion and if you feel that she may not be aware of the restaurant's dress code, let her know. Where I live, it is really easy to pick out the "odd couples" in certain areas, because some guys and gals don't understand what to wear to not draw attention. Most providers are great, just make sure yours doesn't show up in a minid dress with cleavage down to her belly button and f-me heels, and you should also avoid the OG Pimp look if possible... 
- Your first date with a provider is probably not the best night to have a 12 oz. steak... Try to keep it light: having a lot of food in your stomach doesn't make for a great "afterparty".
- Unless both of you find the aroma of garlic and onions emitted from your partner's mouth intoxicating (this should be confirmed before placing your orders!) it is best to avoid dishes that have those spices.
-If you are going to have beans, lentils, scallions, carbonated sodas, or anything else that may give you gas, you better take your Beano with you... lol
- Sharing a few drinks is great, as long as you can both handle it. Look out for both of you and make sure you are both in a fully capable state... Everything is more fun when you have full control of your body and all your senses are not dulled by anything. 
- A good escort can make you feel like you are on a "real life date" with a woman who really, really cares about you. It is her job. You should use this as your "me time" and enjoy the attention. Resist the temptation to turn it around and start prying about her personal life, because she is most likely not in a position to share a lot of the details. If she seems to avoid certain subjects, take that as your clue that you've stepped into murky waters.
- If for some reason you feel that the chemistry is off and the date is not going well, there is no physical attraction and you can't see yourself going through with the rest of the date, speak up. Most reputable ladies will work with you on this and will give you a reasonable refund and let you be on your way. Not everyone is a match.
- If all is well, when you get back to the hotel room, do your happy dance. SCOOORE! lol
I hope you enjoy your first time!