Can an Institution evaluate a consumer for various of its credit products with only one credit report? What if consumer only solicited one product?

No - you cannot use a legitimately pulled credit report for marketing purposes.

Even if evaluation for all would be performed at the same time? As soon as consumer solicits one of the credit products?

Read this and then come back with any other questions:

https://www.ftc.gov/sites/default/files/...0fcrareport.pdf

Read page thirteen under Review Purposes, but the same thing applies when you get a an application for credit that gives you a permissible purpose for that transaction only.

Also read your credit bureau contract.

So does that mean that if I pull credit on a vehicle loan application and notice that there is a mortgage against a property that I can't ask them about it and offer our mortgage products to them?

Not based on the credit report, that is marketing and is not a permissible purpose.

Hopefully that mortgage debt is also on the application you have for credit.

But even still, they would need to present the pitch to everyone, not just those with higher credit scores or you might have a fair lending issue.