##C, <s>112</s> 111 bytes

<!-- language: lang:c -->

    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!=0)&&((l>7)&&(l<10));}

Returns 0 if invalid, 1 if valid. <a href="https://tio.run/nexus/c-gcc#FcpBDoIwEADAu7@ABLILbcIWEo2l@BDjgSiE0rWaFk/Et6Oc5jLbLKxwgvUI96kPRcSVTVwCDx4i6vEVwBrWc8saXWkgXueyvMnmhAXYji5WyrMk1GFYPsEn4DIizHNwial2gbvjLrdUIerv4dlbD7i@g/XLCGn2SMWfmkgpVdeNSve1bT8" title="C (gcc) – TIO Nexus">Try it online!</a>