Learn English – When you tell a joke and nobody laughs

The metal rod is called a skewer. (If it's a bigger rod, designed to hold entire animals and rotate, it's called a spit.)

I would say that cooking over an open fire is called roasting; cooking over a fire on a metal grate is called grilling (or barbecuing, although barbecuing may imply the use of some kind of marinade or barbecue sauce).

Cooking over an open heat source with meat on a continuously rotating spit is called rotisserie cooking.

When meat is on a skewer, that can also be called a kabob, particularly when meat and vegetables are mixed together on the same skewer.

That all said, there is plenty of room for overlap and confusion. One can roast in an oven, or can make barbecued chicken in a crock pot. One can also grill in a frying pan. (Grilled cheese sandwich, anyone?)

Cooking terms are often chosen to indicate the type of heat source, the direction of the heat source, and the dish being prepared.

As for the scenario you described (open fire, using a skewer, no grill or grate), I'd probably call that roasting, although it would be hard to argue for a single, universal "best word" – cooking is simply too diverse for that.

I'll be referring to the definitions of count from Oxford Learner's in my answer.

Don't count is the closest to an opposite for count in the sense of numbering in sequence (definition 1). There's no pure antonym here; what could be the opposite of saying "1, 2, 3..."? Some thesauruses list words like guess as antonyms for this case, but I strongly disagree with that.

Definition 2 means calculating a total by summing up the number of members. This is the sense used in your example (let's count... ten in total). As with definition 1, there's no true antonym, for the same reasons. Similarly, you can get the right essential meaning with don't count, and it would be correct to use in your example:

And thus, if you don't count me, you are nine.

But we can get better results with definition 3, include. Exclude is its appropriate antonym. It's also correct to say it in place of discount in your example:

And thus, if you exclude me, you are nine.

Using exclude causes a definitional shift in the usage of count (changing from 2 to 3), which technically changes the meaning. Outside of situations where semantic pedantry is part and parcel (e.g. the law, professional philosophy, ridiculously close linguistic analysis, internet arguments), nobody will care about this. Everyone (discounting those who don't know enough English) will grasp the meaning without any problems.

Since you've discounted don't count, exclude is the best choice.

Definitions 4, 5 and 6 all have the same antonym: discount. See definition 1 from OALD, which I actually find rather lacking; discount can also mean ignore, not include, minimize, etc. MW is more complete here.

Discount is in your example. While semantically (and grammatically) correct, discount is too formal for the context, making the response sound strange. For a group of people organizing a trip together the phrasing just sounds weird, though the meaning is clear. Using discount makes count definitionally shift, as exclude does. However, here the "distance" between the definitions is noticeably greater and makes the change awkward; in general conversation, people will stumble over this. Exclude is a better choice.

OALD redirects uncount to the entry of uncountable noun!

That's because it's a standard abbreviation for uncountable [noun] in dictionaries. But as you've found out, it's not a word in and of itself.

You've clarified that you're after le mot juste to complement count. I agree that count/exclude and count/don't count aren't as eloquent as a cognate pair, such as include/exclude. However, I'm afraid my vocabulary's at an end here; I don't know of a single-word, etymologically related antonym for this sense of count.

For a simple drop-in replacement, I recommend exclude or don't count. I realize that's not what you're after, but in terms of an easy, quick and accurate solution this is the best way to go. Additional apropos alternatives:

• Use include / exclude instead of count / antonym-of-count.
• Restructure the passage to use with / without me or something along those lines, as suggested by Damkerng T.

If your heart is dead set on some sort of count pairing, you could use discount, but I think it's self defeating to use an awkward, contrived sounding phrasing for the sake of preserving a nice juxtaposition of vocabulary. If you're going to do so, I suggest using counting/discounting and upping the formality for the sake of making things marginally less peculiar. Something along these lines, for example:

OK, we are ten, counting everyone, but mind that I might have some unavoidable work that day. Discounting me and planning for a group of nine might be wise. Please arrange for the food and accommodation accordingly.

Bear in mind that while these sentences are now consistent and don't mix registers, they are still too formal for the context. Someone planning a vacation with friends and who's been using phrases like you guys should expect to receive some quizzical looks if they start talking in this fashion.