Which is faster between a 4gb PC3-10600 and a 2gb PC3-12800?

So I have Lenovo G40-30 and it has an Intel Celeron N2830 @ 2.16GHz 2.16GHz processor and 2gb DDR3 PC3-12800 x1 of RAM. I know right off the bat it's kinda low-end. So I'm planning to add more ram.
Sorry for the quite noob questions, seeing that I've only recently learned about the differences between RAM frequencies:

Is a 4gb PC3-10600 better than a 2gb PC3-12800? I've noticed that there's quite a price difference between a PC3-12800 and PC3-10600.

Also, my laptop has two memory module slots, can I install two memory modules with mismatched frequencies? Like a 2gb PC3-12800 with a 4gb PC3-10600 for a total of 6gb of RAM?

Yes you can, but the 12800 will be downgraded to 10600. Its always best to match, and its better to have 1 4gb stick than to have two 2gb sticks.

Depending on your motherboard will determine what type of ram you can install, how many ram slots you have, how much ram can you can have in each slot, at what speeds.

You can look it up on the manufacturers (motherboard) site or tell us so we can tell you the specifications. Or if you or nobody can't figure it out, you could just use the ram scanner on crucial or newegg sites just to be %100 sure.

Note that laptops have different types of ram as desktops (different connectors).

DDR or higher, higher GB, higher speed, rams will be more expensive.

No you don't want to mismatch ram. For one it may not work. If it does work it will not work in dual channel mode and the better ram will be clocked down to equal the slower ram.