First third of the night, prayer times, and nafl prayers

Assalamualaikum Wa Rahmatullahi Wa Barakatu

1. {If I'm doing anything wrong then I need a detailed explanation on:} just how exactly do we calculate the 1st 1/3 and the last 1/3 of the night? How I've been doing it is I would start by timing when I see the first visible star at the beginning of Maghreb and when I would first see the break of dawn at the beginning of Fajr, and then calculate how many hours is from the start of Maghreb to Fajr. Is what I'm doing right? Please let me know.

2. May I get a detailed explanation on when the beginning and ending of both the preferred and mandatory times of Dhuhr, Asr, Maghreb, Isha, and Witr are? I've watched a video on SalvationArk's YouTube channel concerning it but I still have trouble understanding it completely for some reason.

3. Is it only after the first third of the night has passed that we can pray 8+ rakats of nafl followed by 3 rakat Witr or can we pray as much nafl we can anytime after we performed the Isha prayer but only perform the Witr after 1/3 of the night has passed?

Jazakallahu Khair.

Salam, this link will help you know when it’s midnight and the last third of the night. You just enter your magrib time and fajar time and it will calculate it for you.

thirdofthenight.com/

Jazakallah

May Allah reward you with goodness my brother, thank you

Assalamualaikum Wa Rahmatullahi Wa Barakatu

wa alaikum as-salam wa rahmatullahi wa barakatuh, 

1. {If I'm doing anything wrong then I need a detailed explanation on:} just how exactly do we calculate the 1st 1/3 and the last 1/3 of the night? How I've been doing it is I would start by timing when I see the first visible star at the beginning of Maghreb and when I would first see the break of dawn at the beginning of Fajr, and then calculate how many hours is from the start of Maghreb to Fajr. Is what I'm doing right? Please let me know.

What you described is very similar to how Muslims in the past determined prayer times. They observed the time of Maghrib and Fajr, and in between, they tracked the positions of the moon and stars to estimate the last third of the night. 

2. May I get a detailed explanation on when the beginning and ending of both the preferred and mandatory times of Dhuhr, Asr, Maghreb, Isha, and Witr are? I've watched a video on SalvationArk's YouTube channel concerning it but I still have trouble understanding it completely for some reason.

Each prayer has two times:
a preferred (optional) time and a constrained (necessity) time.

The preferred time for ẓuhr begins when the sun passes the meridian—its sign being the shadow’s inclination toward the east after reaching its shortest length—and it ends when the shadow of an object equals its length from the time of that inclination, which is the beginning of the time of ʿaṣr.

The end of ʿaṣr is when the shadow of an object becomes twice its length.

The time of maghrib begins with the sighting of a night star and lasts until the disappearance of the red twilight, which marks the beginning of ʿishāʾ; its end is the passing of one-third of the night.

The beginning of fajr is from the appearance of the spreading light rising from the direction of ʿAdan toward the qiblah until just before sunrise by the amount of time needed to perform one rakʿah.

The time of necessity is whatever remains outside of these periods.
Whoever catches one rakʿah of fajr before sunrise has caught the fajr prayer, and whoever catches one rakʿah of ʿaṣr before sunset has caught it.

One should not pray during the time of necessity except for a clear excuse.

The funeral prayer and voluntary prayers are disliked at three times: at the time of zenith, at sunrise, and at sunset.

wa salam

Jazakallahu Khair my brother