About the Infinitive

[Natadtw1]

Is it correct that
a) the verb in its infinite form "to be" is never used after the core verbs "to see" and "to notice"
e.g. I looked at his hands and saw they WERE trembling.
Melanie saw that the man’s clothes WERE torn in places.
Are there any other verbs after which "to be" is not used?

b) if "to see" and "to hear" have indirect meaning, such as "to understand, to come to the conclusion" and "to get information that", the infinitive can not be used?
e.g. I heard that Jacob had returned to live in his Oklahoma hometown. (i.e. I got information that)

Are there any other similar exceptions for the use of the infinitive?

Thank you, Natalia