Combination of the present perfect and the simple past?

There is no 'combination' of tenses here, just a coordination of main clauses. Main clauses in coordination are permitted different tenses.

This is completely acceptable. This usage is normal--you might catch any normal American combining the sentences this way. With this being said, I think it would be most normal for this combination to be used in answering a question.

I have checked --> The person speaking has completed an action that perhaps they were asked about: ("Did you check?") or perhaps if someone else was accusing them of not having checked: ("Why didn't you check?").

I found out --> The person speaking is letting the person asking know what they found out.

If the person speaking is volunteering the information, or bringing up the topic, it would be more natural to say: "I checked with several sites, and I found out that it's seemingly some jobless old Latino, definitely not Willis."