Recently I discovered, that if I need to see if variable is even ( or odd ), I could just see if last bit of variable equals 0. This discovery, when implemented, replaced few modulo 2 calculations and thus, whole function ran faster.
Are there any other "tricks" like this one, where working with bits could replace other calculations, leading to improved function execution time?
I doubt that replacing the use of modulo-two calculations by the equivalent bitwise operation produced faster execution times. Any C++ compiler worth its grain of salt will compile n % 2 and n & 1 to identical machine instructions.
Beware of using bit-twiddling hacks as an optimization. First, it's not always clear that the function you are optimizing is a bottleneck. Second, the resulting code is usually harder to maintain and more likely to be incorrect or have subtle bugs. This is what is meant in the famous quote Knuth quote "We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil." Save your effort.
If you truly must pursue this subject, Bit Twiddling Hacks contains a nice list of interesting hacks.