First of all, there is this question and answer that might be relevant:
Were all of Earth's minerals created before Earth's formation, during, or after?
Also notice the bit about "mineral evolution". If you dig more into Bob Hazen and colleagues work, they have some paper where they estimate how much more minerals are expected to exist that we have yet to find.
Tachylite's answer is mostly correct. I'd like to add a few more things though:
And how many combinations of metals/elements are possible to form minerals which doesn't exist on Earth
Hundreds of thousands. There are 90 something (relevant) elements in the periodic table, some of them have different oxidation states, which basically makes them behave as different elements. For example S2- and S6+ are both sulfur, but they are completely different mineralogically. This leads to almost infinite amount of possible compounds and minerals.
And what could be the reason that they don't exist on Earth?
The conditions are not correct. Mineral stability is a function of temperature, pressure, bulk composition and fugacity (activity) of certain volatile components such as oxygen, sulfur, etc. Only a limited set of combinations of those is available on Earth, so that's why they might not exist here.
Also, several minerals are known from synthetic experiments to occur in the Earth, and actually a large amount of of the Earth's mantle is predicted to comprise of them. Two examples are ringwoodite and bridgmanite. Both were first synthesised in a lab, and were found in meteorites. Ringwoodite was only recently found as an inclusion in super-deep diamonds, and bridgemanite was not found yet in the Earth. We do know that the mantle is full of that, it's just not accessible to us.
This is similar to all of the Fe minerals that are found in meteorites. It's likely that Earth's core is composed of a bunch of Fe minerals we don't even know yet, but they are not accessible to us so we basically can only guess based on experimental studies.