1. I assume you mean exempt, rather than non-exempt. If they only qualify as non-exempt, then they MUST be classified as non-exempt. IF they qualify as exempt, they CAN be classified as exempt but they MAY be classified as non-exempt.
An exempt employee is almost always paid on salary; they receive their entire salary every week (except in a very few, rigidly controlled circumstances*) no matter how many hours they work. They do not get overtime. If they only work 27 hours, they still get their entire salary; if they work 70 hours, they ONLY get their salary. They have no expectation of overtime EVER; they CANNOT be docked except in the circumstances already outlined.
A non-exempt employee MUST be paid for every hour that they work; however, they do not have to be paid for any time that they do not work. If they go home early, come in late, leave for a doctor's appointment or a child's school activity; they get docked. Conversely, they MUST be paid overtime for every hour they work over 40 in a week (and, since you are in CA, over 8 in a day). It IS legal to pay a non-exempt employee on a salaried basis, but ONLY if they also receive any overtime due.
2.) I don't know how to make this any more plain. An employee whose job duties classify them as non-exempt can ONLY be classified as a non-exempt. An employee who qualifies as exempt, can be classified as EITHER exempt or non-exempt as the boss chooses.
4.) If he chooses to classify them as non-exempt, then he must treat them as non-exempt, which means keeping track of their hours (either by time card or other method) and paying OT as earned. If he chooses to classify them as exempt, then he need not keep track of their hours OR pay overtime, but he may do either IF he chooses to.
As to your third possibility, if he is classifying them as non-exempt, then he must keep track of their hours somehow. It does not HAVE to be via time cards, but that is the easiest and most accurate way to do it, and whatever method he chooses must be accurate under the law.
These answers are not going to change no matter how many times you ask the questions. I don't care how much you want the answer to be that he must treat them as exempt if they so qualify - he doesn't. You can ask the question forty different ways and it's still going to come out that if he chooses to treat them as non-exempt, he can; also that at this point, we have no way of knowing (at least I don't) whether they actually could be treated as exempt. It's entirely possible, based on the information in your post, that he is correct and he DOES have to treat them as non-exempt under the law. Regardless of whether he has been given good or bad information, everything he is doing is legal. Don't neglect the possibility that he is claiming that he doesn't want to deal with time cards but is required to under the law, only as a justification (since a number of people believe it is somehow "better" to be exempt - it's a status thing). I understand your anxiety over this issue, but I am not going to answer these same questions again.
* An exempt employee can have his salary docked under the following conditions:
1.) It is either the first or last week of employment and the employee does not work the entire week
2.) The employee is on FMLA
3.) In a company with a bona fide sick time policy with a "reasonable" number of days (undefined in the statute but generally accepted as at least 5 and preferably more) the employee has already used all the sick time that he has or has qualified for, and then calls in sick again
4.) The employee takes a full day off for strictly personal reasons
5.) The employee has been suspended for a major safety violation (effective August 23 of this year, the limitation to a safety violation is lifted and the employee can be docked if he has been suspended for any disciplinary reason)
