I'll assume that by the term verbals you mean verbs, modals, auxiliaries, and participles. :D
1. The past tense and the past participle forms of regular verbs are always the same.
regular: walk walked walked
irregular: break broke broken
It appears to be true. Mind you, there's always an exception somewhere.
2. Verbals used as auxiliaries are never used in any other way.
Well, hmm, what about the verb 'to be'? Technically it's a helping verb, but it functions as a main verb in copular structures: Pat is a doctor.
3. Verbals as well as verbs may be classified according to tense.
True, but 'tense' is a fuzzy term. How should we define infinitive verbs? As tenseless? Furthemore, what about mode? Is 'may' present or future? And what about 'might'? Is it past or future or present?
4. In a sentence with at least one dependent clause, a verb in the present tense must always be followed by another verb in the present tense.
False. An example would be nice. :D
5. An auxiliary verb is a helping verb, one that is used with another verb that is important.
An aux is a helping verb. True.
An aux can be used with another verb. True.
That the other verb is 'important' sounds strange.