I think your first doubt was taken out of context from the following rule (excerpt from The Buddhist Monastic Code, page 370):
Should any bhikkhu teach more than five or six sentences of Dhamma to
a woman, unless a knowledgeable man is present, it is to be confessed.
“Then Ven. Udāyin, dressing early in the
morning and taking his bowl and (outer) robe, went to visit a certain
family. At that time the lady of the house was sitting in the main
entrance, while the daughter-in-law was sitting in the door to the
inner chamber. So Ven. Udāyin went to the lady of the house… and
whispered Dhamma into her ear. The daughter-in-law thought, ‘Is this
monk my mother-in-law’s lover, or is he being fresh with her?’ Then,
having whispered Dhamma into the ear of the lady of the house, Ven.
Udāyin went to the daughter-inlaw… and whispered Dhamma into her ear.
The lady of the house thought, ‘Is this monk my daughter-in-law’s
lover, or is he being fresh with her?’ After whispering Dhamma into
the daughter-in-law’s ear, Ven. Udāyin left. So the lady of the house
said to the daughter-in-law, ‘Hey. What did that monk say to you?’
“‘He taught me Dhamma, ma’am. And what did he say to you?’
“‘He taught me Dhamma, too.’
“So they criticized and complained and spread it
about, ‘How can Ven. Udāyin whisper Dhamma into women’s ears?
Shouldn’t the Dhamma be taught openly and out loud?’”
The two factors for the full offense here are:
1) Object: a female human being who knows what is and is not lewd, what is well-spoken and ill-spoken, and who has not asked one a question about the Dhamma.
2) Effort: One teaches her more than six sentences of Dhamma without a knowledgeable man present—i.e., a male human being who also knows what is and is not lewd, what is well-spoken and ill-spoken.
Summary: Teaching more than six sentences of Dhamma to a woman,
except in response to a question, is a pācittiya offense unless a knowledgeable
man is present.
Your second doubt, seems to be referring to this rule (excerpt from The Buddhist Monastic Code, page 356):
Should any bhikkhu have an unordained person recite Dhamma line by line (with him), it is to be confessed.
This is an offense with two factors:
1) Effort: One gets a student to recite Dhamma line-by-line with oneself (which, as we shall see below, means to train the student to be a skilled reciter of a Pali Dhamma
2) Object: The student is neither a bhikkhu nor a bhikkhunī.
Summary: To train a novice or lay person to recite passages of Dhamma by
rote is a pācittiya offense.