"Wedi" has the sense of "I have gone", "I have seen", etc. It literally means "after". "Dw i wedi mynd." is literally "I'm after going."
But we can also directly past-tense conjugate the verbs themselves, for a sense of "I went", "I saw", etc. For example, "Dw i'n canu" ("I'm singing") can become "Dw i wedi canu" ("I have sung"), but it can also be conjugated directly as "Canais i." "Canais" being the past tense (first person singular) form of "Canu".
"Mynd"'s conjugated past tense forms are just highly irregular. Instead of "Myndais i", "Myndaist ti" or the like, it's "Es i", "Est ti".
When you get to Past Tense 3 has an explanation of the simple past tense forms by person and number - apologies if you've already got there! You're correct that in this case the last vowel is dropped and -aist ti is added though.
This course is designed to support a course called Cwrs Mynediad - e.g. Past Tense 3 notes says "This unit teaches the simple past, y gorffennol cryno, and it supports Cwrs Mynediad Uned 16." They might explain things in greater detail. Available in app form here: http://www.cwrsmynediad.com/.
There's also a good Wikibooks course (no need for app or subscription) that explains all the grammar here: https://en.wikibooks.org/wiki/Welsh
Quick note: the Wikibook wrongly claims that 'u' is pronounced like French 'u' or German 'ü' in the North of Wales. It's actually like Polish 'y' or Russian 'ы'. But in the South it's the same as 'i', so you needn't worry too much about it. And it seems otherwise correct.
For most verbs, yes! For most verbs, drop the final vowel, or the final -ed, or the final -eg, and add the appropriate person and number and number marker.
(I can think of at least four ways to form the past tense in Welsh, mind. >.> Wedi, conjugated past, bu, and roedd.)