Legal Question in Business Law in California

No.

No, unless the pro se (or in pro. per.) is also a duly-licensed attorney.

The terms "pro se" or "in pro. per." (the former more commonly used in the Federal courts, the latter more common in state courts) more or less literally mean "for himself" or "in his own person" and, by definition, exclude the possibility of representing another person or entity.

However, let me hasten to add, the Court of Appeal has decided that an answer filed on behalf of a corporation by an unlicensed person (e.g., the corporation's president) is sufficient to prevent a default, although subject to demurrer or other objection. By analogy, it may well be that the filing and service of a complaint on behalf of an entity such as a corporation or limited partnership by an unlicensed person would be sufficient to stop the running of the statute of limitations. I do NOT recommend this!

Sooner or later, if an entity wants to sue or defend, it will need a lawyer.

I would just add that in Federal Courts there is not a right even to represent yourself. It is at the discretion of the judge. In California state courts, you are entitled to represent yourself, and a business that you own as a sole proprietorship. Anyone else and any other kind of business entity, including partnerships, must have a lawyer.