My apologies if the question sounds stupid, but I am trying to understand the extent to which SSL certificates secure the contents(or activities done over SSL). Here is my understanding; please correct me if this is wrong.

Under a hypothetical condition:

1. Person-A is the Administrator of a windows laptop.
2. Person-B is a non-admin user of that laptop.

My understanding:

When person-B visits a CA-Signed SSL certified site(https://example.com), the activities(Eg: writing a comment, etc) done within the site are hidden(encrypted) from everyone including Person-A(admin), however, Person-A may see the site names Person-B visited.

If the above is true, is it also applicable when Person-B visits a site with a self-signed certificate if person-B trusts the self-sign certificate?

I am trying to understand the extent to which SSL certificates secure the content (or activities) over SSL. Here is my understanding:

Under a hypothetical condition:

1. Person-A is the Administrator of a windows laptop.
2. Person-B is a non-admin user of that laptop.

My understanding:

When person-B visits a CA-Signed SSL certified site  (https://example.com), the activities  (Eg: writing a comment, etc) done within the site are hidden  (encrypted) from everyone including Person-A  (admin), however, Person-A may see the domains Person-B visited.

If the above is true, is it also applicable when Person-B visits a site with a self-signed certificate if person-B trusts the self-sign certificate?