I'm not a grammar expert, but I would say "there's a thing and I don't know what it is" or "there's a thing but I don't know what it is."

I'm not a grammar expert and English is not my first language but I think I used to say this before and I just ended up taking out the "what it is" and changed it for the thing I'm trying to remember:

There's a thing that I don't know the name of

Or

There's a thing that I don't know how to describe

Or

There's a thing whose purpose is a mystery to me

Is that what you're refering to? Sorry if it's not. I don't think any of the first three examples are correct, or at least they sound really weird to me.

Please do correct me if there's an English mayor somewhere though!

Simpler: I don't know what this/that thing is.

Basically trying to say: there's this thing that I can't remember the word for/don't know exactly, but I know it exists and need it for context.

It is awkward, but many dialects compress, forgo, and bastardize sentence structure depending on where you're at.

This is a great question, and it led me down a bit of a rabbit hole. This kind of clause is called a Gapless Relative Clause. The sentence could be written as you have it, or with "I don't know what it is" - the "it" is called the Resumptive Pronoun which are "common in spoken English but are officially ungrammatical".

The Wikipedia article has a similar example:

In other cases, the resumptive pronoun is used to work around a syntactic constraint:

They have a billion dollars of inventory that they don't know where it is.

In this example, the word it occurs as part of a wh-island. Attempting to extract it gives an unacceptable result:

*They have a billion dollars of inventory that they don't know where ___ is.

Here's another great article I found which sums it up well:

"Resumptives are non-standard, but in such cases they're much better than their gapped counterparts, which people usually find incomprehensible, or at least very hard to comprehend."

So basically, your original sentence is "unacceptable"/"incomprehensible", but adding "it" would be grammatically incorrect but easier to understand. Best bet is probably to totally rephrase the sentence as others have suggested.

Best sounding recommendation probably depends on context and ‘the thing’:

There’s a concept I don’t understand.

There is something in the box I don’t recognize.

There is a feature of the coffee machine I haven’t figured out yet.

There’s a Greek word in the original text that I don’t know.

Describe the situation in context. None of those phrases sound natural.

There's a thing and I don't know what it is.

The closest phrase I can think of is: "There is a thing of which I do not know."

Awkward af phrasing, though, as others have stated.

I don't know what that thing is.

I don't know what that thing is for.

I don't know what that is.

Any of these work for what you are trying to say?

I don't know what this/that thing is.

What dis? Da fuq?

"There's a thing which I can't identify"

or

"I don't know what this is"

There's a thing I can't identify.

There's a thing I don't know about.

There's an unfamiliar thing.

All the formulations you wrote indeed sound either ungrammatical or unwieldy to me.

I don't think I've come across that before, but I'd say it depends on what is meant:

• I don't know what that thing is.
• There is a thing, but I don't know what it is.
• There is a thing such that I don't know what it is. I.e., I do not know what all things are.

There may well be some other ones, but I don't know what they might be.

I'm struggling to think of a context where you'd say this where you couldn't just say "I don't know (about) that thing" or "there's a thing I don't know".

That there is a thing is kind of implied.

There’s a thing of which I know not what it is

If you want to be a bit poetic: There’s a thing I know nothing of.

What is this thing? I have no idea what it does.

"There's an unfamiliar object"

To keep as much of your original sentence as possible, "There's a thing, (I don't know what it is,) and...."

Basically the only way to smush those two concepts together in the order you'd like is if one is basically an interjection to an ongoing sentence containing the other. In that case, you wouldn't use any connecting words at all.

If you wanted a single sentence, many other commenters have already given great suggestions.

There's something there/here that I am struggling to describe/understand.

Part of me feels like this is a question surgically designed to make someone go insane.

It sounds OK if you say it in French

"There's a thing I'm unfamiliar with"

If you don't know, I sure as hell don't.