For example, in a sentence like 'he looked at his enemy....(use the verb fall)', would one say falling or fall? I feel like if the sentence was watched, it would be fall, but now for this construction I am not sure. Is there a rule or something that dictates this?
You can use only FALLING here.
There is a group of verbs connected with feeling, hearing and seeing can be used with -ing or with an infinitive without to:
So after the verb LOOK we can use only -ing.