Yes, this is normal for Hilton. There is no problem with booking multiple one-night stays, and the rate will be what you are quoted for each night.
For a longer stay, it is worthwhile to check all variations (one night stays, two night stays, and so on) to find the cheapest combination.
Another advantage of multiple one night stays is that if you have to cancel part of the stay, it is easy and you can keep the nights that you need.