Quincy's becoming Vizards and Arrancars

Could a Quincy ever become a Vizard or an Arrancar?

Vizard: You have to be a Shinigami then win fight against your inner hollow to be able to use most of its power.

Arrancar: You have to die and become a hollow, then remove your mask.

-Now I don't think a Quincy could become a Vizard because he/she would have to become a Shinigami first... But I do think that it is possible for a Quincy to become an Arrancar.

-If a Quincy were to become an Arrancar, do you think that he/she would still retain their Quincy powers?

Your logic is sound but you forget that its in the world of bleach and Kubo is allowed to do whatever he wants and pull out any Deus ex machina he wants whenever he wants even if they make absolutely no sense.

So the answer is yes anyone can become a Vizard or Arrancar.

I thought Quincy could become Shinigami because Shinigami are just souls of the dead.

And no, a quincy would not retain powers if turned into an arrancar. Arrancar don't have any skill they had while they were alive.

I'm going to say yes but they won't have quincy powers afterwards

I agree with this~
and i think the quincy power will still remain~

They can become Vizards and Arrancars and still have their quincy powers. Quincy's are basicall humans who are aware of their spiritual powers and gather spiritual energy from their surroundings (since they don't have enough of their own). So if a quincy were to die and be a Vizard or Arrancar. They would still be able to use their quincy techniques. Probably..

Basically a Quincy Arrancar/Vizard
=
Their own spiritual energy + energy of their surroundings = Super Saiyan

Ths is of course if they ever remember that they were a quincy when their souls become a hollow/shinigami

I'm going to say yes, since anything seems possible in Kubo's world of Bleach. So a Quincy becoming an arrancar or shinigami is very likely to happen. Except we would probably never know he/she was a Quincy unless Kubo wanted to inform us that.