Yes, you can have two instances of Eclipse running at the same time. However, they can't both access the same workspace at the same time. If you try to do this, the second instance will complain about it on startup and ask you to choose a different workspace.
Also bear in mind that Eclipse tends to be a very memory-hungry application. Running two at once may put a significant strain on your system.
As long as each project uses its own workspace, yes, you absolutely can. This assumes that your system has sufficient memory and CPU resources to accommodate multiple instances, of course. (I do it all the time!)
If you want to open different work spaces with different projects then Window -> New Editor; here you can open different work space with different project.