Yes, insofar as even that corrupt regime sought 'to punish those who do evil and to praise those who do good' (v14). Peter's argument doesn't depend on there being a Christian government (there wasn't in his day) that rules with perfect justice. Rather he assumes that even pagan authorities maintain some sort of law and order, and this is for our good. Presumably shoplifting was illegal under the Nazis, and you would find yourself in court for murder. So to the extent that what they punish as wrong is what God thinks is wrong, then yes, you should submit. But if the SS ask you for the addresses of your Jewish friends, then of course at that point you should refuse.
Yes, but not by firebombing it. We (unlike Peter's first readers) live under a democratic government, and as such we all share some responsibility for the rule of our country. As such, Christians should take seriously their freedom to vote, and are also free to lobby the government to make laws that stay close to God's idea of right and wrong. We should be appalled at the current state of the law on abortion, and its failure to protect the lives unborn children. But in our protests against it, we must stay within the law. We may protest taxes, but not by failing to pay them (cf. Mark 12:13-17). We may protest against abortion clinics but not by lawless means.
Not necessarily. The modern relationship between employer and employee won't correspond in every respect to the slave-master relationship of the first century, and we don't have an obligation today to submit to every whim of our employer - for example, if your boss were to specify whom you should marry, or what kind of breakfast cereal you should eat, that would be outside his/her remit. I would suggest that we are to submit to the authority of our employer insofar as the request they are making lies within their legitimate sphere of authority. They can tell you what colour binders to use for your project, but not (probably) what colour socks to wear! How exactly this applies to staying late at work will depend on the job - if you are a nurse, it goes with the territory that you have to work shifts, and some of those may clash with Bible study. If you have signed a contract to say that you will stay in the office indefinitely to meet a deadline, then you will have to honour that commitment. But in other cases, it won't necessarily be the case that at your boss's request that you stay beyond your contracted working hours lies within their authority (even if they assume that it does). It may sometimes be right to choose to disappoint your boss, rather than to let down your wife or your small group at church.