I think acquiring a company and then cutting non-essential staff is pretty common sense. I think the idea of cutting people to save money is pretty standard across all big companies. Companies like Microsoft, Google, Salesforce, AWS all hire a lot and then cut them to save money, especially recently.
Outside of Elon tweeting a lot about his Twitter adventures, his practices seem pretty normal for someone who has just acquired a company.
And as far as the Twitter API going down today, it came back up pretty quickly. So obviously the staff that he does have in place managed to get it resolved in a timely manner.