wordplay - I never knew my words could speak!

^{This is an entry to the Fortnightly Topic Challenge #25: wordplay.}

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^{"These words! – they come falling free; / speech: daft here, deft there..." — Emrakul}

You know, I've kept some words. Words that work for me. No no, they aren't really my slaves; more like, my pets. They never said they don't like my job or anything; besides, they can't actually do much except what they're told to. They do all sorts of chores for me: like, say, recording a dispute in the past, or cleaning my room. They can even lie to my amazing old relative (he's is one who won't believe), and scold him.

So today morning, as usual, I went to their cage...er, room to take them out and sort out their duties. What I saw there totally blew my mind. I never knew that my pet words could speak! For themselves!

Here's what they seemed to be saying:

Did G contain H? _L
C's got hold of T, and happens to be E. _R
D equals at least one of C and itself. _C
Regarding N: does G contain H? _L
M stays indoors because of itself. _C
G, P, R – they all happen to be NT. _C
Inside G, L is the same as T. _L
When placed near H, E becomes T. _L
H equals at least one of T and Y. _R

Now, of course, there are people who "talk" to their pets; frankly speaking, I'm not among them. I didn't even know that my pet words could speak! Seriously, I'm very confused right now.

Just what do these words want to say?

Answer

The first thing to note is ...

... that there are some words in italics in the text above the quote: recording — dispute — past — cleaning — lie — amazing — relative — one who won't believe — scold

These are the definitions for the clues that are given in the quote. These clues must be reworded so that they spell single-word answers. For example, "G contains S" could be rewritten as "S in G" and give the answer SING.

Did G contain H?

WASHING — cleaning; was H in G?

C's got hold of T, and happens to be E.

CHASTISE — scold; C has T, is E

D equals at least one of C and itself.

DISCORD — dispute; D is C or D

Regarding N: does G contain H?

ASTONISHING — amazing; as to N: Is H in G?

M stays indoors because of itself.

MISINFORM — lie; M is in for M

G, P, R - they all happen to be NT.

GRANDPARENT — relative; G, R and P are NT.

Inside G, L is the same as T.

LISTING — recording; L is T in G.

When placed near H, E becomes T.

ATHEIST — one who won't believe; At H, E is T.

H equals at least one of T and Y.

HISTORY — past; H is T or Y.

The subscript letters ...

... indicate one of three possible positions: L (left), C (centre) and R (right). When we take the letters from the answers at these positions, we get:

leftmost letter of WASHING → W
rightmost letter of CHASTISE → E
central letter of DISCORD → C
leftmost letter of ASTONISHING → A
central letter of MISINFORM → N

central letter of GRANDPARENT → P
leftmost letter of LISTING → L
leftmost letter of ATHEIST → A
rightmost letter of HISTORY → Y

The words want to say:

We can play.