My guess is she would have been the woman Red-verse Nathan had invited to be Finch's dinner date.

Assassinating Obama with a drone would be a bit on the nose…

I was expecting Synecdoche to end as follows and disappointed when it didn't:

The threat that Samaritan identified was Finch closing access to the machine. He's doing it because he doesn't want Root to find out what he's up to.

It was significantly different circumstances. In Deus Ex Machine, the government was on trial, and there were innocents he had to protect. Remember it's his hatred of the government that is his primary drive. Having the government on trial would have (secretly) appealed to him. The same way that selling a closed…

A further piece of evidence to support the 'Finch is perpetrator' theory is that it is Samaritan who identifies a threat to itself prior to the phone call to Reese and Fusco near the start of the episode.

The reason you're confused about Harold's 'procrastination' is that you're coming from a faulty premis. Harold doesn't go Linus because his friends are dying - they've been effectively at death's door from the start of season 4. Harold becomes Harold 2.0 because he got caught. And not only did he get caught, but the…

You clearly haven't seen Person of Interest.

His number did come up. Finch is carrying the photographs in the hospital when Reese bumps into him.

They did, in "Zero Day". It's the reason Ernest Thornhill was created.