Carbocation stability + determining position of attack on a carbocation in SN1 reaction
It is important to note that the two structures shown aren't actually different. That's what resonance implies that in reality, it exists in between both of the as a 'hybrid'.
So it is not right to state that the nucleophile attacks on the left structure 'or' the right.

Coming to the carbon, (again, it's not right to take the structures to be different)

&quot;I just don't know why the methanol attacks the $\ce{sp2}$ carbon in the right structure instead of the carbon with the $+1$ formal charge on the left structure&quot;

It's actually the same carbon! and the hybridisation is still $\ce{sp2}$ no matter what, as the carbocation is also a planar species($\ce{sp2}$). And this is where the attack occurs.


&quot;I'm also not sure why the MeOH attacks the carbon next to the carbocation and not the oxygen itself, where it has the positive charge&quot;

'Carbon next to the carbocation' ? I believe you are confusing the +1 formal charge on oxygen to be a carbocation which is not true( Carbocation has the positive charge exclusively on Carbon) .
The attack is ocuring at the carbocation.

Our nucleophile here, is $\ce{OH-}$ while oxygen only has a +1 formal charge and also, the positive charge is more localised on the carbon as Zhe mentioned.
This is because oxygen being a more electronegative species, doesn't really 'like' the positive formal charge on it.
But still,

&quot;doesn't the nucleophile attack the carbocation, or whichever atom bears the positive charge?&quot;

Well, a nucleophile is a species that donates electrons at electron deficient sites. But oxygen still has it's lone pair! and the $\ce{OH-}$ will face repulsions from them if it tried to attack here.
The real electron deficient species here is only the carbocation and thus it is the preferred site for attack by the nucleophile.