Maybe I'm an idiot, but no matter how much I Google I can't seem to grasp the
concept of か being used mid-sentence. I've already run into it a number of
times. Like here:

> アメリカやヨーロッパなど６つの国は、イランが核兵器をつくろうとしているのではない **か** と考えて、経済制裁を続けていました。

I believe this roughly means...

> Six countries within the Americas and Europe, thinking that **perhaps** Iran
> shouldn't be trying to create nuclear weapons, continued with economic
> sanctions.

From what I understand, か here indicates an embedded question. Like in
English, "I know **what** you mean." It can also indicate uncertainty with the
speaker in conversation. This comes from a news article though (admittedly for
kids, haha), so I'm thinking I'm incorrect in assuming that last part.

Also, I've seen it here in this sentence:

> 夏にちょうどいい名前だね、と何回言われたこと **か** 真夏はバレエの準備をしていた。

My attempt is roughly...

> Manatsu, who was told her name was perfect for summer **how** many times,
> was practicing ballet.

I guess what I'm asking is whether or not I have this thinking right. If I
don't, please correct me and try to put it in super simple terms because I
feel like I'm not going to get it otherwise. I've been struggling with this
for awhile, hah.
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2016-03-08T01:50:21.223
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particle-か
Usage of か I keep encountering
There are a few situations one would use か mid-sentence. For example:

1) 私は電車 **か** バスで行く。(I will go either by train **or** bus)

2) ぼくがだれ **か** 知ってるか。(Do you know **who I am**?)

In the first example, you can use か if you are deciding between two things. In
the second example, in answer to part of your question, yes, you can use it as
an embedded question.
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> アメリカやヨーロッパなど６つの国は、イランが核兵器をつくろうとしているのではないかと考えて、経済制裁を続けていました。

As already mentioned in a comment, [the exact sentence has already got
detailed explanation](https://japanese.stackexchange.com/q/30560/7810). One
point is, か doesn't stand as "question word" but represents the intention of
question or doubt itself. Japanese "indirect" quote always follows the grammar
of direct quote, so the most faithful translation would be like "thinking
'Isn't Iran going to make nuclear weapons?'"

> 夏にちょうどいい名前だね、と何回言われたことか真夏はバレエの準備をしていた。

This sentence is on the borderline of ungrokkableness. If I were asked if it's
grammatical, the answer is definitely **no**. Don't write such kind of
Japanese! :)

The most reasonable interpretation I can think of is the part before か is a
monologue of 真夏 turned into narration. It doesn't seem to clearly modify
anything in the rest, an extreme case of [dangling
modifier](https://en.wikipedia.org/wiki/Dangling_modifier).
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