I'll try my best to answer your questions :3
No - the PS3 has forced whole drive encryption whereas the PS2 supports optional encryption on a per-partition basis. This is only used in a small number of cases, for example the Install Data of Final Fantasy XI. I'm not sure about the actual algorithm but judging by the fact that l_oliveira has managed to extract files from a raw dump I'd say it's weaker than the PS3.
1. Is the PS2 drive encrypted the same as PS3?
The PS2 runs a single user operating system so there are no logins or users. I do believe that each file is time-stamped though.
2. Do you know how the login / user history is saved ?
As far as I know there's no chronological list as there is with the PS3 (history.xml) however you can at least have an idea which applications have been used by looking at the "Save Games".
3. Do you know if the PS2 keeps browsing history the way computers do?
As for how to proceed, I would advise connecting the HDD to a PS2 with a write blocker and using uLE to read the filesystem as it'll be able to give you as much detail as possible with regard to time-stamps etc. You may have to modify the case as I doubt there's a write blocker small enough to fit in between the drive and adapter while it's connected in the usual way
 Install(s) Done Since 6th December 2010