How would i differentiate between the pronunciation of fagel versus fageln?
You can hear the 'n' at the end of fageln if you heard very closely. I agree with you, it's not easy to recognize the two words.
Shouldn't it be fågeln är dricker?
No, we don't have that construction. Both "The bird drinks" and "The bird is drinking" are translated "Fågeln dricker".
Just out of curiosity, when people type in sweden, do they type informally and just drop the accents on the letters or are the accents crucial to understanding what a word means.
They're not accents - åäö are letters in their own right. The å is as different from the a as the p is from the q in English. Swedish natives would never use aao in place of åäö because it makes zero sense to do so.
So this is sort of an irregular noun?
Because it ends with en so it can't be fägenen.
No, it ends with -el.