Why can this not be "O benim türüm"?
Unfortunately, it doesn't really sound idiomatic here. Really, "tip" is the best version in this case. It just has to be memorized as an idiom :)
But in most cases are "türüm" and "tip" interchangeable?
The key in that they are interchangeable in most cases. This is one case where that is not the case. :)
Usually those words that keep the last consonant are one syllable words.
Would this still be pronounced as "o benim tibim"? Or is the "p" really preserved here?
The "p" is preserved. Some words keep the unvoiced consonants and they just have to be memorized as they come along.