Alphanumeric Line and Curve Counting
Haskell, 214 199 188 175 bytes

 g 0=[]
 g n=mod n 5:g(div n 5)
 d#s=sum[n|c&lt;-d,(i,n)&lt;-zip['0'..]$g s,c==i]
 f s=(s#0x300BBD37F30B5C234DE4A308D077AC8EF7FB328355A6,s#0x2D5E73A8E3D345386593A829D63104FED5552D080CA)


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The numbers of lines and curves are the digits of base-5 numbers and stored as base-16 numbers. Function g translates back to base-5.

Edit: -13 bytes thanks to @cole.