Yes, the sentence is grammatically correct and sounds natural.

Yes, it is but to make it sound more natural I'd say "after two hours of searching, I was so glad when I found my passport."

Hello , I'm an Indian native English speaker. i would love to help your child improve his fluency and develop his communication skills in English so that you can reach your goal. i am willing to meet your needs and help you in every possible way. Feel free to message me back and check out my profile. Cheers:)