I want to know if I can split guitar string gauges, ie. using 12s on the bottom and 10s on the top, both for standard and drop tunings.
Sure, you can, but there are some considerations you should be aware of.
There are already hybrid sets of strings that have this done for you.
Take a look at Ernie Ball Skinny Top Heavy Bottom. These have the EAD strings from a heavy gauge set and GBE strings from a light set.
Ernie Ball STHB (Skinny Top Heavy Bottom) have the EAD from a set of gauge 12, so the E=52, A=42, D=30. And the GBE from a set of gauge 10, so the G=17, B=13, e=10.
D'Addario also make a set of Light Top / Heavy Bottom (EXL140) with the same gauge strings as STHB.
Hope this helps.