1. No
2. No
3. No
4. No

My business scans for Hilton rates from 18 countries, loggined in, not logged in, Diamond, Gold, Silver and Blue accounts. There is nothing that influences pricing on the hilton website. There may be a flash or strategic sale that pops up at a certain time of day but this is something planned that you would need to know to look for. To my knowledge there is nothing like you describe.

OTA might do this but Hilton does not from my experience of over 100,000+ searches on the hilton website.