It is down to a dealer's discretion, although massive discounts, if found out by Rolex, could prove to be a black mark against an AD. Rolex have a brand image to look after, and they price their watches at a level they feel they should be sold at - if you start discounting by massive amounts, it devalues the brand. It may be excusable in very rare cases, but if it started being a regular occurrence, then the AD can probably say goodbye to their relationship with Rolex. The margins really aren't massive on a Rolex, so it's not in a dealer's interest (given the high overheads and running costs involved with owning a prime luxury shop) to be selling Rolexes at huge discount.
As for authority, there is a deal of authority up to a degree - we just have to use our heads. For bigger discounts, it's best just to ask first rather than blunder in and get a telling off afterwards
If buying more than one, as in any business deal, bigger discounts make sense. I love selling multiple watches at a time, even if we make less than if we sold them individually
My advice for a first time buyer is to do your research. Make sure you know your product, that you know exactly what you want, and a price you'd ideally want the watch at. You can't always get it at the price you want, but if you talk about what you want with confidence and authority, you might be able to get a good deal. Take as long as you need to make your mind up - if that's one visit or twenty one visits, any salesperson worth dealing with will deal with you patiently, and want to help you make a final decision without being pushy
If you have been looking at a watch for a few weeks, and that same watch has had a price rise, then yes, it can be a springboard to get it at the old price at least. We're reasonable people after all, and it's not fair to expect you to pay one price one day, and a higher price the next for exactly the same watch. There's maybe a two week window after a price rise to negotiate like that
Hope this answers your questions sufficiently