Thor has the standard powers of a GOD. Because he is one. He specializes in certain areas, but that doesn't mean he lost all ability outside of those areas.
More exactly, Thor is an ASGARDIAN. He is on par with all the existing pantheons of Marvel. However, in their own definition, they no longer have the sheer scale of True Gods. They can have an influence in their portfolio, but, for example Odin is no longer capable to create Earth from the bones of Ymir.
No mistakes, they are extremely powerful (Thor managed to go toe to toe against ONE celestial), but they don't have the sheer SCALE of a god and they don't receive energy from prayers, nor are they able to hear them.
Because by that standard, Thor himself would not be worthy to lift the hammer.
Correct, the concept of "worthyness" was never truly explained in Marvel, but going by example, Taylor Hebert pre-skitter and post-Khepri is as worthy as Captain America and the Marvel Thor. Both are true heroes willing to make the personal sacrifice and completely behind protecting Earth and Humanity. (the cap is well the the Captain, Marvel Thor is the direct son of Odin and the Goddess of Earth).
That would be redundant. It might even be a downgrade to the hammer.
Well... i would say yes and no.
Mjolnir was NEVER truly equaled in the entire Marvel universe (besides Stormbreaker, its copy and the shield of Marvel Captain America).
However, even being a magical weapon and able to break through the dimensional protections of the Endbringers and Zion, the Sting would greatly help Mjolnir.