Yes.
Swelling is normal for a new piercing.
Bleeding after getting a new piercing is normal; a piercing is technically an injury & your body will (usually) heal.
The size of a normal earing.
Your nose may be dry. This is not normal. Buy a humidifier and seek doctor.
It sounds a bit worrying. You should probably keep an eye on it.
It is called a nose piercing.
Yes, you can use ear piercing cleaner on a nose piercing.
No no, all you need to do is to clean your piercing after you're done since sweat gathers bacteria rather quickly when not dried. Bleeding happens when you remove and re-insert the piercing wrong, otherwise you should be fine.
Yes, you don't bleed a lot when you get a piercing.
no prodigy doesn't have a nose piercing
your nose piercing should effect you in no way when you eat.