Yes on parliament being able to propose its own laws. It is such an easy and straighforward reform that would give the EU a lot more democratic credibility that I am surprised it has not happened.
Also surprisingly, yes on the directly elected commission, but it is a very hard question.
My reasoning is:
a) It would give the EU a lot of democratic credibility, even if at a big cost.
b) After the fact that the Spitzencandidat process was killed, I have lost faith that the EU can function as a parliamentary democracy, so a presidential style one is probably the lesser evil at this point.
Of course, a directly elected comission comes into a lot of problems. The biggest one being the electoral system. I can't see a straight popular vote being used. Maybe the EU could use some sort of Electoral College, but I think we all know how well that works
Another option would be each country choosing its own commissioner via popular vote, but I have no idea how it would work to pick the president of the comission.