Arranging visit visa (self sponsored resident)

Usually, it is businesses that can sponsor or apply for these duration visas.  There is, literally, a section on the paper form which asks for business details like CR, address and also the business stamp (if the business is not registered as an evisa sponsor).

No idea about self sponsorship changes but I wouldn't be surprised if the answer is no.  And yes you are right; while you can be the guarantor, a separate sponsor is needed.

However, you can get family members over on the usual evisa route.  Only downside is that the visas are shorter duration and not as easy to extend.  Another alternative is to do this through travel agents / tour operators which obviously has cost / flexibility issues.

Suggest to also check with immigration at the Manama office in the off chance that something might have changed.

Evisa sponsor registration
Yes, as per this, individuals are not authorized to be a sponsor.

Problem with evisa is that it asks purpose of tour . Tourism, business , investment etc. mentioning family visit is not possible.

Yes family visit is generally sponsored on the paper forms with company stamps.

By family evisa, I meant that you can ask them to apply for a standard tourist visa and specify that they will be staying with you.  I believe that they would have to attach a copy of your CPR data print out.

My sister in law did it this way a few months ago.