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同じ人が書き込んでいないか

I think it means something like

Didn't the same person make this post (bulletin board)

I'm not sure however. What do you think ?

1

いないか can't make sense by itself, unless combined with previous 書き込んで to mean its progressive or result ("is not posting" or "(has) not posted") followed by か.

か is a question particle, but I guess here it's used as indirect question "whether —". English has only one word "whether", but Japanese has two options using positive + か or negative + か. The difference is somewhat like that of "Do — ?" and "Don't — ?" were carried into indirect question form; the positive + か expects the positive case is more frequent or typical, and the same applies to the negative. Usually the difference can hardly go beyond subjective nuance, but in specific cases it becomes crucial:

書き込む人がいるか心配だ I worry how many people would make posts (wishing for post)
書き込む人がいないか心配だ I worry lest somebody should make posts (afraid of post)

So translation would be (depending on context):

whether (perhaps) the same person is posting
lest the same person should be posting

0

This is the negative form of progressive tense plus the question marker か.

It represents that it is in the state of 書き込む (being posted/being written).

I think your translation is good :).

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