Well first things first the mechanism for electrophilic substitution for activated pyridine should be like this :
Now I think I understand why the ED strength of -OMe and -NH2 makes no difference. It's because the positive charge is not static . There's a delocalization of the Pi electrons due to resonance , correct ?
It sounds like you already understand this but just to clarify, the reason they have different electron donating effects is because nitrogen is less electronegative and therefore more "willing" to donate it's lone pair and take on a positive charge than oxygen. So the intermediate with an amine group benefits more from that electron donation and has less carbocation character.
I'm not sure I completely understand the logic in your explanation but it's not what I had in mind. My observation was that your molecule has a special kind of symmetry which gives exactly equal distribution of attack via electrophilic addition. I'll try to explain without a picture: Think of things in terms of probability. Obviously there's a 100% probability of substitution with each successfull reaction. Let's say for the sake of explanation that oxygen is worth 40% and the amine group is worth 60%. And we'll also assume ortho and meta occur with equal probability (this is close to true). Next cut each percent in half and assign it to each location on the ring. You'll notice the probability of substitution at each location ends up being 50%. This math will work with ANY set of values you assign to the two groups.
This would NOT be the case with a 1,4 substituted benzene ring. In this case the para position is blocked and you'd see preferential substitution ortho to the amine group.
I hope that wasn't too convoluted but it's the best objective way I can think of to explain it.
Now if the medium is acidic , shouldn't N get protonated resulting in N+ -H ? This in effect changes the electrophilic attack to C2 or C6 , thereby the obtained product is not the one shown in my 1st post . Is this logical ?
I'm not familiar with the numbering on pyridine but you have the correct general idea. The protonated nitrogen no longer has a lone pair to donate. Now inductive effects dominate and it becomes meta directing. Inductive meta direction is generally weaker than direction provided by lone pair donators like oxygen. This means the sum of the products resulting from ortho/para substitution relative to the oxygen would be greater than the product resulting from substitution meta to the protonated amine.