What's the meaning of 龙舟队分哪个两个组？

龙舟队分哪个两个组？ is simply incorrect.

The combination of 哪个 and 两个组 doesn't make any sense grammatically and logically.

哪个 means WHICH ONE, for example: A B C D, 哪个是B？(which one is B?). The second one is B.

哪两个组 is right, means WHICH TWO GROUPS?

So the correct sentence is 龙舟队分哪两个组？

分 often comes with 为：

她让学生每四人分为一小组。
She asked the students to split into groups of four.

Just thinking about a question yesterday on the origin of tense words in Chinese and whether the teams divide themselves or 被分为. Certainly, a team is a team and remains undivided.

龙舟队被分为哪两个组？
The dragon boat teams are divided into which two groups?

龙舟队分为哪两个组？
Dragon boat teams divide into which two groups?

But, if the team is divided after some fashion, my piercingly nautical suggestion would be:

比较胖的队员全部坐在右舷，瘦瘦的队员都坐在左舷。
Fat team members all sit on the starboard side, thin team members all sit on the port side.

龙舟队分哪个两个组？

I think it is a typo.

remove the extra 个 and write 龙舟队分哪两个组?(dragon boat teams divided into which two groups?) make the most sense

龙舟队分[哪两个组]?

龙舟队分[男子组和女子组]

龙舟队分[成人组和少年组]

龙舟队分[业余组和职业组]

It is wrong to use 个 (a) as a classifier for 两个组 (two groups)

Similarly:

你說的是哪兩个隊 (O)

你說的是哪兩隊 (O)

你說的是哪个隊 (O)

你說的是哪隊 (O)

你說的是哪个兩隊 (X)

你說的是哪个兩个隊 (X)(X)

I think this sentence is not perfectly grammatical. You can analyze it as follows:

龙舟队 The Dragon Boat Team

分 (divide into, assign to)

哪个 which (one)

两个组 two groups

It doesn't sound grammatical to me mainly because 哪个 means "哪（一）个 which one", but the subsequent noun phrase is about "两个组 two groups".

We can probably read it as "which two groups", but then the Chinese would be “哪两个组”.

As additional evidence, Googling the quoted “哪个两个组” phrase yields a good 5 results, against 84k for “哪两个组”.

Anyway, putting it all together it becomes something like:

Which two groups is the Dragon Boat Team assigned to?

or

Which two groups is the Dragon Boat Team divided into?

In both these cases, I think 分组 is not a separable verb. Why?

In a separable verb the separable part is the object of the sentence (that's why they are also called verb-object phrases) but this object has a non-specific meaning (some linguists call it virtual or ostensive object), and as such, in English it's often rendered as a 1-valency verb. Compare:

我吃饭 = I eat food

我跑步 = I run steps

Instead your sentence already has an object — or if you prefer, the subject of a passive form —, which is 龙舟队 ...unless you want to argue that 龙舟队 is who performs the division in groups. (The fact that 龙舟队 is the topic of a topic-comment construction doesn't affect its grammatical role.)

As a counter-test, can you rewrite 组 in a 把 + Obj. + V structure? You can't. Instead 龙舟队 can be placed after 把:

他把龙舟队分哪两个组 (ok) vs 龙舟队把组分哪两个 (???) (not ok)

So what is 组 then? I think it's the object of a 3-valency result complement structure. This is relatively easier to see if we rewrite the verb+result in a copy structure, instead of topic-comment. (This is similar to what you can do with degree complements):

(主语) 分 龙舟队 分（成/到） 哪两个组

This is my analysis. Any feedback is welcome.

龙舟队 --- (The) Dragon boat team

分 --- separated / grouped into

哪个 --- which

两个 --- two

组？ --- groups?