I've got three questions related to the use of the verb "will" in the meaning of "to wish":"Dear Pig, are you willing to sell for one shilling
Your ring?" Said the Piggy, "I will."
1. Why did the pig, being asked, "Are you willing...?" answered, "I will", not "I am"? (Provided we were to abstract from the rhyming "оn the hill" in the following couplet)
2. Is the verb "to will" in the meaning of "to wish" way too outdated nowadays?
3. If it is not, does it require the to-infinitive to follow?
The last question comes from the comment of maestro of the English language Colin Fine which I chanced upon on the ELL Stack Exchange site:
If, for example, I visited the lake often over a period of a few weeks, I might will say they "were living" there (implicitly, over the period when I was visiting).