“Equip elderly professor for final battle” (10)
Nice.ARMAGEDDON = arm aged don
Martian country missing its premier is in state of isolation. (10)
An easy one:
Cleans up scattered studs (5)
A little harder:
Securely fastens around about fifty large containers (7)
Cleans up scattered studs (5)
DUSTS anag.Securely fastens around about fifty large containers (7)
BAR(RE-L)S, RE = about, L = 50
Mr. Zotti scoffed after introduction to Straight Dope (6)
Monster needing no introduction and goddess of discord acquire location of stone statues. (6, 6)
Very nice!
EASTER ISLAND
BEAST -B + ERIS + LAND
Sketch a reversed trophy. (5)
Ah, that helps!
Answer:
HANDBOOK
Explanation:
Snare (HOOK) traps ANDB (annoyed “band”)
Answer:
MPSIMS
Explanation:
British politician in this case is MP (Member of Parliament)
MP is on SIMS (name of a popular video game)
Here’s a new one:
Removing Ford model from lairs – how offensive! (7)
Removing Ford model from lairs – how offensive! (7)
[spoiler]HIDEOUS
HIDEOUTS (lairs) minus T (Ford model)[/spoiler]
Cafe Society sent into orbit, surprisingly (6)
Award - “Draw” (=sketch) + “a”, reversed.
Yay, I got this one too!
That must mean that something is wrong with the clue. Given how this thread is going. 
shouldn’t it be more like :
Sketch a reversed trophy, with tail removed. (5)
Or, is it
Sketch a beheaded trophy, reversed. (5)
You’re mixing wordplay and definition.
In the original, (Sketch a reversed) is the wordplay and (trophy) is the definition.
In yours, (Sketch) is the definition and (a reversed trophy, with tail removed) is the wordplay (and the answer would be 4 letters, not 5).
ETA: Or, rather, the definition and wordplay should not be mixed, so splitting the clue like so: (Sketch a reversed) (trophy, with tail removed) isn’t normally kosher.
Peace officer scams place to eat. (9)
CONSTABLE
Oh man I never thought I would get one of these. (At least I think I got it.)
Yep. You got it.
Guns shot young women blocking the light. (10)
[spoiler]SUNGLASSES
Am I right that “shot” indicates the anagram?[/spoiler]
Does it guess easy, preciousss?
“Observe monarch on quest” (7)
seeking
Scots sailor goes in reverse on this surface (6)