There is no real separation between the company and its owners. If the owners fail to maintain a formal legal separation between their business and their personal financial affairs, a court could find that the corporation or LLC is really just a sham (the owners' alter ego) and that the owners are personally operating the business as if the corporation or LLC didn't exist. For instance, if the owner pays personal bills from the business checking account or ignores the legal formalities that a corporation or LLC must follow (for example, by making important corporate or LLC decisions without recording them in minutes of a meeting), a court could decide that the owner isn't entitled to the limited liability that the corporate business structure would ordinarily provide.
Oh yeah, definitely. There shouldn't be any mix of assets. You need to keep them separate if you're trying to make the legal case that they're separate.
Even an LLC with just one person operating it (Which the IRS still sees as a sole-proprietorship I believe) still has their personal assets covered.