there is no pre-defined rule however is up to the immigration officer as you should get a proper long term visa for your stay instead of abusing visa exempt.
The basis of financial evidence is for proof you are financially responsible and have liquid cash for yourself in case shit happens. Hence investment account wont be accepted.
not sure what you mean, but you have mentioned you are on non O visa, and later said you are on visa exempt. which is which?
you can only hold 1 visa at any one time, and if you leave the country without applying for reentry, your non-O visa will be cancelled. Simple as that, dont try to be smart and look for loopholes.