Can I increase the L2 cache memory of my CPU?

"the L2 cache is built into the CPU itself. The only way to get more is to replace your CPU with one that has more L2 cache.

The Celeron is more of a budget class processor compared to your C2D, so it makes sense that it has less cache.

Will more cache be faster? In most cases, yes.

In the case of your desktop, depending on the socket you can replace the CPU with a new unit that not only has more cache, but with a faster clock speed as well."

No, no and yes, in that order