What does 44' mean in BIP44?
I believe 0x8000002C is 128 as an integer


... No, it isn't. First of all, it already is an integer, just represented in hexadecimal. In decimal it is 2147483692. How did you get 128?


  how does this equate to 44' however?


44' means that hardened keys should be used. The distinguisher for whether a key a given index is hardened is that the index is greater than 2^31, which is 2147483648. In hex, that is 0x80000000. That is what the apostrophe (') means.

The 44 comes from adding it to 2^31 to get the final hardened key index. In hex, 44 is 2C, so 0x80000000 + 0x2C = 0x8000002C.


  I also believe that the ' means that it is a "hardened key", is it hardened because 128 is between 0 and 2^32 - 1 ?


No, hardened means that the key index is between 2^31 and 2^32 - 1. Between 0 and 2^31 - 1 are unhardened keys.


  Which means that the only key that can derive it, is the private key?


Yes.