In US English, it is always HAS. For the second, you will hear THEY. Yes, COMPANY is singular, and THEY is plural, but that is how we speak. It is understood that a Company has many decision makers, bosses, etc so that is where THEY comes from. Thus, the antecedent for THEY is understood and not stated. If you were writing formally and not speaking these two sentences, you would likely try to formulate it another way.

"Company" can be either singular or plural, depending on whether you are considering it as a single entity or a group of decision-makers. You need to be consistent, though. So, your sentences could read something like this: The company have introduced new rules for their employees. They have also taken on a new CEO to run the company. or The company has introduced new rules for its employees. It has also taken on a new CEO to run the company. NB If you are writing for an American audience, you should choose the singular option. Otherwise, either option would be fine.

The company has made new rules for the employees. --> or more precisely: The company's board (or board of directors or management) has made new rules for the employees. It also introduced the new CEO to run the company. (This sentence works better if you say "the company's board" in the first sentence.)