Li Shenron
Legend
No to all three because of these:
"The GM calls for an ability check when a character or monster attempts an action (other than an attack) that has a chance of failure. When the outcome is uncertain, the dice determine the results."
"A character can only provide help if the task is one that he or she could attempt alone."
"Moreover, a character can help only when two or more individuals working together would actually be productive."
These are enough for a DM to handle each situations in their preferred way without any house rules. Nowhere the RAW says that a PC has the rights to make an ability check, not even on her own, much less for helping another.
As an example, nowhere in the rule it says that just because your PC has an Intelligence score, she must be granted a check to recall a piece of magical knowledge i.e. what we normally would call an Int(Arcana) check. The DM can simply say the outcome is certain that such character won't recall some knowledge she never had in the first place. This means she could not attempt the task alone, and thus cannot also help someone else. But even if she could attempt the task alone, the DM can still say that working together would not be productive.
You can't rule every situation of ability checks with exactly the same rule (core rule or house rule), you would always have several situations that do not work with such rule, because all ability/skill checks are not born equal.
