A few Persona 5 questions.

I have a few questions about Persona 5 as I just ordered the game.

1 - Before the fight with Fake Igor (true ending) is there a save point or do I have to go back and do some kind of dungeon to get to him again (note I don't even know if there IS a dungeon or not before him or if you just go to the velvet room and start)?

2- Is it like Persona 4 where if you die in a dungeon or on a boss you go back to your last save? If so, can you kinda manipulate your saves by saving a few days before the deadline in another slot so if the deadline comes and you decide you are underpowered you can go back and spend some of the days that you were with friends grinding instead?

Thanks