If an older person who has clear signs of mental impairment was to enter into a contract for investing and becoming 1/4 owner in a company, who's son is one of the other 4 people, how should it be done?
This question is beyond vague (even aside from the poor grammar).
What does "clear signs of mental impairment" mean?
Enter into a contract with whom?
Is the contract at issue
both "for investing" and for the purpose of this person "becoming 1/4 owner in a company"? In other words, is the person investing money and, in exchange for the investment, becoming an owner of the company? Or are these two things separate?
How much money is the person investing (both in terms of dollars and in terms of percentage of his overall net worth)?
What is the business entity form of the company (e.g., corporation or LLC or something else)?
What does "the other 4 people" mean? You wrote that the person will become a 1/4 owner and that his son is also an owner. So there are three other owners (5 total)?
What is your involvement in this situation?
And, finally, what does your question mean? Are you asking us how this vaguely described transaction should be documented?
Can a court-appointed guardian sign something like that?
Depends on the terms of the guardianship order. Is there a guardianship in place at this time?
Is there a better option?
Better than what? Better for whom? Better for the "older person"? Better for his son? Better for the company? Better for the company's other owners?