Can I share CPU over network?

At a fundamental level, the answer is yes, but you can't do this in the way you are thinking.

Supercomputers use this tactic to provide incredible computing horsepower, but they are nothing more than a cluster of regular ol' computer systems (called nodes) that cooperate to process a particular task. They have control software that farms out individual work units to various nodes to be calculated independently. The CPUs in such nodes are not communicating with each other per se. An application running on one of the nodes is coordinating the work, much like a project manager would coordinate the members of a team to complete a project.

Such a supercomputer setup requires:

• An operating system that is designed for this purpose, installed on each node in the cluster.
• Control software that can parcel out the work to each node and coordinate the result data received from them.
• An application that can break a problem down into discrete work units, written in the control software's language.

So in your situation, no, you can't combine the CPU and memory of your two computers to make Google Chrome perform faster.

This is known as CPU interleaving. I believe you need a compatible BIOS on both devices along with smart cards. However, interleaving is designed to be run over dual port fiber cards (not LAN).