Can VPS be used privately/securely

1) I have never used a VPS before. Can they be nearly as private/secure as a local machine?
For example, if I use full disk encryption and only ssh to communicate, is there any way the company can know what I'm doing/data?
2) I use FDE on my laptop, and after update, I have to type the password before I can boot. So how is this achieved on a VPS as ssh doesn't start before the OS does?
3) Even if I use FDE, the company can read the password during the initial setup right, and also temper the ISO? Can I install/setup ISO locally and then upload image to the vps, so I know the iso is genuine and they did not read my password during setup?
4) Is openbsd a good server os for hosting websites and possibly E-mail?

Thank you!