will hosting provider have access to my dedicated server?
Yes, they will have access to your server. If virtual, they have access through the virtualization console or container root. If physical, IPMI and out-of-band management provide access. They may have access to your backups. They definitely have access to your disks...
In 2000 Microsoft published something very smart and is still (mostly) relevant today. The 10 Immutable Laws of Security http://technet.microsoft.com/library/cc722487.aspx
Rule number three is "If the bad guy has physical access to your computer it's not your computer anymore."
Fact is you should consider any computer you don't have COMPLETE physical and technical control over a potential target for compromise. Here's a link to think on: http://felipeferreira.net/?p=1259
Depends on the provider.
Usually if you change the password they don't have access anymore.
However: They have physical access.
They can just take out a disk from your RAID1 and have all your data.
They can reboot your server and reset your password, or boot from a CD and read it all, ...
If you really need the best privacy you can get, just encrypt the data. As the other answers and comments say, if you don't do that, then there are methods to get the data out of your server.
Yes, they have access to your server.
You could mess around with encryption, a locked cage in a colo, etc. But they can break the locks on the cage, or use DRAC/KVM over IP/whatever. As others have said, if they have physical access to your server they can break into it.
Go with a reputable, high-quality provider, and don't think of it as them having access to your server (which they're backing up for you). Think of it as having minions who will replace bad hardware in the middle of the night for you. If your provider is PCI compliant, this is adequate to the needs of PCI (also HIPAA, FERPA), etc. If your security needs are greater than that, you probably need your own personal data center.