INVADER (driven a*)
+++++
What are you sitting on? Sounds like an Irish tune (8)
DERRIERE (Derry air)
A new beginning is supposedly regarding youth imprisonment country. (12)
Rejuvenation (re + juvie + nation)
++++++
Gold’s omnipotence became complicated long ago (4,4,1,4)
ONCE UPON A TIME (anagram AU + omnipotence)
++++++
I was studying alloys when I heard about someone having a hypersensitivity reaction at the Metropolitan Museum of Art.(10)
Metallurgy (Met + allergy)
++++
See face back in drywall (6)
See face back in drywall (6)
GYPSUM (spy in mug backwards)
+++++
Musical Omelette is minus cast. (4, 2, 2, 2, 5)
Meet Me In St. Louis?
Contains all the letters in “omelette is minus” but seems to be one e short.
That’s it 3 "E"s.
Off Meet Me In St. Louis
Epic wrestler issues rancid elution while going numbers one and two (6)
I want it to be ISRAEL (first two letters of each of “issues rancid elution”) but I can’t make the connection with “epic wrestler”, can anyone help me out?
In the Book of Genesis Jacob wrestled with an angel and was renamed Israel.
Thanks, in that case I will continue!
Emhoff dresses Ford with her Singer? (4, 10)
ISRAEL is indeed correct. I first thought of “biblical wrestler”, but I didn’t want to make it too obvious 
Back to the current puzzle:
ELLA FITZGERALD (Ella [Emhoff] + “fits” + Gerald [Ford])
++++++
Darned disorganized shed stuff! (6)
DANDER (anagram)
The German duplicate is such a pistol. (9)
DERRINGER (Der ringer)
+++++
The Eastern European was relevant.(7)
GERMANE (German + e)
A body part cherishes vociferously these tales.
ANECDOTES (a neck dotes)?
If that’s correct:
+++++++
Tom makes Etsy irritable (5)
TESTY (T from Tom, +ETSY, anagram)
Many mayors oft-times pad their speeches recklessly (9)
STYROFOAM (anagram)
+++++
Ms. Brenneman initially got depressed and laid awake. So emotional!(8)
AMYGDALA (Amy + first letters of next words)
+++++
Eagerness and fervor are in city style (8)