##C, 112 101 bytes
j,i,k,l;f(char*s){l=strlen(s);for(i=l;j<l;)k+=(s[j++]-48)*(i>1?i--:-1);return!(k%11)&k&(l>7)&(l<10);}
Returns 0 if invalid, 1 if valid. Try it online!
betseg
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