Hi,
Answer 1: yes, no level converter needed
Answer 2: if you provide a level converter for other pins, I'd use another one here. Or at least a resistor between the 5v and 3v3 domains.
Answer 3: the EN pin effectively switches off the ESP8266. After changing the EN pin back to high, the chip restarts. So you can obviously use this for saving power but you have to initialize the library every time you wake the ESP8266. You don't need to reset it via hardware reset then.
I searched the internet about the 5V tolerance of inputs (not power) of ESP8266 and many people said they are 5v tolerant in fact but the manufacturer claimed the opposite. Look here: ESP8266 is 5V-tolerant after all? | .Stack | Hackaday.io
My first tests of this library were on Arduino and I used a simple MOSFET level convertor like this:
Edit: another thought about the RST and EN pins: you'd better use open drain output GPIO and you are out of 5v/3v3 problems. Nevertheless, Atmega328p does not have this option, afaik. Here is a trick worth trying: Open Drain - #12 by CrossRoads