What is the simple subject in these sentences? I have a quick question. This is really confusing me.

Pls be understood a bit more.
The second sentence,
–international and American championship titles–
international title –one title
American championship–another title
so both create –titles, two of subjects connected with –And.
So, you need a plural verb—were.
However, what I understand from your question that is you need many morphological matters to understand verb+subject topics.
Pls you should check it out a morphology of grammar book, I mean you need a book that analyses many grammatical matters or you needn’t only a plain grammar book.

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