I think I was close.  Is it a grave?

I'll give you that, but the answer is actually, "gravestone."

I have your name on my face, [the name of the deceased is carved in]
But you will never know; [because you are dead]
Your days are numbered
On my belly below; [dates of birth and death inscribed on it]
And though I may wish you peace, [saying "rest in peace"]
You will reap what you sow.

The reference to the belly bellow threw me me a bit so I hedged.

I have eyes and a tongue,
As it could be put,
But only sometimes it's said,
Do I have a foot;
I have no soul, 'tis true,
But something close thereto,
I may just have one or two.

Is this riddle stumping you guys?

Sorry, I hadn't taken a look at it yet, I've been inactive lately for some reason. I'm losing track of the days, which isn't helping with anything, including schoolwork.

My first guess is a shoe, or a pair of shoes :)

A shoe is correct!

I have eyes and a tongue, (shoe has a tongue and eyelets for laces)
As it could be put,
But only sometimes it's said,
Do I have a foot; (if empty, no foot; if being used, has a foot)
I have no soul, 'tis true,
But something close thereto, (has a "sole," not a "soul)
I may just have one or two. (has a sole and a soul if someone is wearing it)

I rub out worlds,
And destroy equations;
I wipe out ideas,
And the written word--
          --on occasion.
I swipe away all I touch,
Of all not writ in stone--
          --of any persuasion.

An eraser?

yes!

Too easy? How about this one:

What have I got in my pocket?

Schrodinger's cat wearing the One Ring?

Yes! In other words, it was empty...as far as you know!

It's empty as far as you know.  Mwa-hahaha!

As long as I don't check, it's both in the state of knowing and not knowing.

A hammer and anvil have I,
But iron will they never shape,
A stirrup with no feet,
A drum that never beats,
And a canal never seen in landscape.

What a lovely description of some of the parts of an ear

Yes!

I only recognized the last two lines as ear-related. Do you guys have anatomy degrees or something?

Sure: Ear drum and ear canal

Never heard of an ear stirrups, ear hammer or ear anvil, before tho.

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I live in the wilds and catch my prey in a net;
I'm scary and hairy, so when I appear, I cause many to fret;
There are many kinds of me, but not all are toxic;
The best way to defeat me is to try not to panic;

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I have two answers I will accept for the riddle above. Whoever guesses both (first) gets 10 WOTS

These are what the three bones of the inner ear are called.

spider?

Yes! But there is a second answer I've thought of that works too.

Lolth, Queen of the Demonweb Pits!

Good pull but nope. Besides, that's like adding a few more descriptors to spider.

I'll give it up if nobody else wants to guess, and then we'll move on to a new riddle.

Spider was probably the better of the two, because the thing was supposed to be ambiguous and now only vaguely reflects the other choice.

Honestly, I'll just put the answer in spoiler text:

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Spoiler text: (Highlight or hover over the text to view)
YOU FELL FOR IT FOOL! THUNDER CLOSS SPLIT ATTACK! --But actually my 2nd answer was trolls.

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I lick without a tongue,
And crack without a whip;
My form is always changing,
Reaching out with pointed tip.