1) The best way is to use acidic constants, but that's unit 4 knowledge. As far as 1/2 goes, you have a rule of thumb, which is:
Strong acids = complete dissociation = HCl, H2SO4, HNO3
Moderately strong polyprotic acid = H3PO4
Weak acids = CH3COOH, almost everything else
2) The conjugate of NO3- is HNO3, a strong acid. When a strong acid reacts, it is because it is extremely favourable for it to dissociate, like going downhill with a sharp slope. For it to go backwards, you need to go against the original reaction (i.e. going uphills with a sharp slope), which is very hard. Therefore it doesn't happen (or only does so at a negligible rate). This is why NaNO3 is neutral.
3) In solution, they are dissolved ions, and thus are separated from each other. Though for simplicity, you could write
})
, the (aq) implies they are dissolved/separate.
} + Cl^-_{(aq)})
is a more explicit, but nonetheless equivalent, way of saying the same thing.