Python 2, 108 104 92 88 bytes

-12 bytes thanks to Rod
-4 bytes thanks to Kevin Cruijssen

s=input();c=s.count;print[all(c(s[[]>[1]])>=c(o)>1. for o in s)];aaafffillpprrtuu=1.>1.; 

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Python 2, 108 104 92 88 bytes

-12 bytes thanks to Rod
-4 bytes thanks to Kevin Cruijssen

s=input();c=s.count;print[all(c(s[[]>[1]])==c(o)>1. for o in s)];aaafffillpprrtuu>1.>1.; 

Try it online!

Python 2, 108 104 92 bytes

-12 bytes thanks to Rod

s=input();c=s.count;print[all(c(s[1>1])==c(o)>1for o in s)]#### ...1;;>>[[]]aaafffillpprrtuu 

Try it online!

Python 2, 108 104 92 88 bytes

-12 bytes thanks to Rod
-4 bytes thanks to Kevin Cruijssen

s=input();c=s.count;print[all(c(s[[]>[1]])>=c(o)>1. for o in s)];aaafffillpprrtuu=1.>1.; 

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Python 2, 108 104 bytes

def f(s):c=s.count;return[all(c(s[0])==c(e)>1for e in s)]####...111aaadddfiii]][[lloon000ruutt;;;:::=>>> 

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Python 2, 108 104 92 bytes

-12 bytes thanks to Rod

s=input();c=s.count;print[all(c(s[1>1])==c(o)>1for o in s)]#### ...1;;>>[[]]aaafffillpprrtuu 

Try it online!