Based on the news updates from various sources today, here are the major updates on the hearing over PCA's jurisdiction issue over the case of Philippines vs. China:
1. Upon the decision of the Arbitral Tribunal, the Phlippines delegation was requested to answer further questions given by the Tribnual on Monday, 13 July 2015 in Hague. These questions were handed over to them beforehand. This is the final pitch from the Phlippines delegation to the 5-member tribunal before the court decides on whether or not it has jurisdiction on the arbitration case filed against China.
2. Details of the arguments on this 2nd round hearing:
According to the Phlippines' presidential spokesperson Abigail Valte, “It’s really different from what we have. It’s really more of questions, (no argumentation). It’s not an adversarial proceedings kasi. They would just ask questions on your positions I would not call it gisa (argumentation). It’s Q and A, we were given the questions already and then we will be making, presenting the answers today”.  So these additional questions were given before this 2nd round hearing, and the Phlilippines delegation prepared their answers  and presented accordingly.
However, the details are not to be made known to public. No substantive portions of the presentations is supposed to be revealed to the public while the hearing is ongoing. 
However, some news report says "The second round of oral arguments seeks to establish the point that China's claim over almost the entire South China Sea is illegal."  We are not sure the basis this news report makes this remark.
3. Phlippines side responses: "hopeful" and "positive" on the 2nd round of arguments
From the PR (public relations) point of view, all the news reports from the Philippines mentioned the answers were well presented, well explained.
Thus the Phlippines side is expecting a favorable ruling on the jurisdiction issue.
4. Some Filipino media started augment about "provisional measures"
In its case raised against China, the Phlippines reserved a "provisional measures" right, that is the court can be asked to rule a temporary order against China and to request China to stop some activities. , 
The pre-condition is the court has jurisidiction over the case.
Now before the 2nd round of hearing, during a chance interview,  one of the delegation team member, Justice Secretary Leila de Lima, said this is one of the steps being studied by the legal team.
5. The wait on the jurisdiction decision: 1 month, 3 months or 6 months?
In Manila, Foreign Affairs spokesman Charles Jose quoted the contracted American lawyer on the case, Paul Reichler, as saying the decision may come out 90 days later.
Another lawyer in the panel said a ruling on jurisdiction before the end of July. 
However, another news report says this decision might come until end of this year. 
6. The next step:
If PCA decide it has jurisdiction, Manila will then have to prepare for another round of oral arguments on the merits.
One news report  says the Philippines anticipates the final ruling to be either in first quarter or first half of 2016.
Otherwise if the court decides on no jurisdiction over this case, case closed.