You prepared the spell differently and cast them as if you were the class the prepared them.
You can yous any slut to cast them(so if you have multiple AT and one wizard you can upcast burning hands to a level 5 slut even if you only have it as a wizard.
Your slots are different from your known/prepared spells.
The slot are universal and work like the table.
About what you quoted I already answered, the spell are not resisting, there is no such thing.
The JoAT and reliable talent work with counterspell and dispell magic because those spells use an ability check ant those two features boost ability checks.
Most other spells use an attack roll or no roll. If it is not called an ability check it is no boosted.