개 is a general counter that can be used when counting object. In many cases, you can use the counter 개 instead of the specific counter for an object (For example, the counter for pencils is 자루, buy you can also use 개). However, you cannot always use 개 to substitute another counter. For example, when counting machines,cars, and other types of automobiles, you have to use the counter 대.
In short, 개 is a very useful counter and you can count many things with it. Just remember that there are exceptions.
Batchim causes the final consonant in a syllable to sound different when it's the final consonant of a word or is followed by another consonant. In this case ㅊ is pronounced like a ㄷ stop. You can read more about consonant assimilation here: