Will, i.e., 'Liquid Plumber' interfere with my scrap disposal surrounded by any channel? The drain seems stopped up in the trap below the rubbish disposal?...

The drain seems stopped up in the trap below the rubbish disposal? The disposal runs, but the water does not go down.
Will scathing chemicals hurt the rubber or mechanics of my garbage disposal? Thanks!
No.
It will vandalize a stainless steel sink though.

But 'Luquid Plumber' isn't that good.
What is available at plumbing wholesale houses is.
Thrift brand cleaner, is some wicked cleaner.
most chemicals on the market will not clear drains properly - a drain cleaner and or plumber is truly the best way to fix any drain issues - i would be more concerned on your sink draining versus disrupt to the disposer - most disposers have metal inner components that rust as it is, a non draining drain will not help the disposer out - your best bet is to disconnect the drain pipe from the disposal to the wall and clear the clog. afterwards re-connect the pipes. if the pipes under the sink are chrome looking, be carefull not to break the pipes. also, put a drain pan below the sink before you loosen the pipes so you don't make a mess.
Answers:    FIRST ~~~~> READ THE DRAIN CLEANER'S LABEL!!

generally solution drain cleaners say not to use them in a disposal!!

the "ONLY" time i recommend fluid drain openers is when the drain slows a bit. once stopped, DO NOT USE THEM!
NO IT WONT HURT YOUR DISP. AND ALSO WONT CLEAR MOST BACK/UPS
BUT IT WILL LEAVE A FUNKY SMELL IN YOUR HOME.