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I have found the following definitions:

怀疑 [doubt; suspect; scepsis]

疑惑 [feel uncertain; be not convinced], and it is additionally defined as "Puzzle" and "Unpeaceful"

From what I feel the former is more about skepticism, while the latter is more about uncertainty

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  • "汉语动词380例"has the pair 怀疑/疑心 but not 疑惑(all 3 in CIME), according to which "疑心" 和 "怀疑2。"的意思相同,可以互换,where 怀疑2(cf. answers):王丽怀疑是有人敲门。"怀疑"在这儿是猜测别人做某事的意思。又例如:a。我怀疑今天要下雨。b。听口音,我怀疑他是广东人。"怀疑"表示猜测的意思时,通常不使用否定形式。
    – user6065
    May 2 '17 at 14:24
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怀疑 is a verb for 'to suspect'

Example: 我怀疑他杀了他儿子 (I suspect he killed his son)

怀疑 is also a noun for suspicion (2.the state of mind or feeling of one who suspects)

Example: 这只是我的怀疑 (It is only my suspicion)

疑惑 is an adjective for 'uncertain (2. not confident, assured, or free from hesitancy); puzzled'

Example: 你这话使我感到疑惑 (these words of yours make me feel uncertain)

疑惑 is also a noun for ' doubt; uncertainty; puzzle'

Example: 有疑惑 (have doubt) ; 重重疑惑 (layers upon layers of uncertainty); 这个疑惑 (this puzzle)

嫌疑 is noun for 'suspicion' (4.state of being suspected)

Example:他有杀了他儿子的嫌疑 (he is under the suspicion of killed his son)

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Yup, you've got a good handle on it.

Here's the entries as they appear in Pocket Oxford:

怀疑

<动 名> doubt, suspect

引起怀疑

arouse suspicion

我怀疑他今天来不了

I have a hunch that he won't be able to come today


疑惑

<动> feel uncertain, not be convinced

疑惑不解

feel puzzled

I don't know where you get the meaning unpeaceful from for 疑惑, but other than that you're going in the right direction.

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