In my jurisdiction, which is not Pennsylvania, it is sometimes possible to serve process by publication. There are some pretty specific requirements for exactly how this much be accomplished. This confers limited jurisdiction to the Court, in that the Court may grant a divorce and award child custody, but may not divide marital property or award child support, because those issues require personal service of process.
In Scenario #2, in my state, if the defendant has been properly served, she has 30 days to respond. Once that time runs, if she has not responded by filing something with the court, she is not entitled to any further notice. Plaintiff may proceed to have a hearing, at which plaintiff must testify and produce at least one corroborating witness to establish the grounds for a fault based divorce. If the Court finds the proof is sufficient, the Court will grant the divorce and all of the other relief requested in the petition (assuming personal service of process, otherwise see above for limitations regarding process by publication). In my state, it is not possible to obtain a no fault divorce without the consent of both parties. If Plaintiff is unable to prove he is entitled to a fault-based divorce, the parties will remain married.
In Scenario #3, again limiting to my comments to my state, it really depends on what exactly the defendant does, and whether children are involved. If defendant misbehaves in open Court, or fails to comply with a temporary order, she may be cited for contempt, and may go to jail for a (usually short) period of time.
If she appears to have some sort of mental illness, she may be committed or required to submit to a psychiatric evaluation. If she is found to be incompetent, the Court may appoint a Guardian ad Litem to protect her interests. Plaintiff will have to consider what he wishes to do next very carefully. Insanity is a ground for a fault based divorce, but if a divorce is granted on that ground, Plaintiff may be ordered to pay for Defendant’s care. If children are involved, a Guardian ad Litem may be appointed to protect their interests as well…and it would not be the same lawyer acting as GAL for the incompetent Defendant. Court appointed GALS are paid by the parties, so the litigation will get considerably more expensive.
Your state probably does things a little differently than we do, so you’d need to check with an attorney licensed to practice up there to see how such things are handled in PA.