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Looking at your site I'd say they are all necessary because only WPML core can't translate page builders or custom fields. You can look here: https://wpml.org/purchase/
If one of the features you need is not available for the multilingual Blog, then you need both String Translation and Translation Management.
If this doesn't help, I would also need your WPML debug information. You can find it in:
WPML -> Support -> click on debug information link
Then you can copy/paste the text you see in the Debug box I'll enable for the next answer.
More information here: http://wpml.org/faq/provide-debug-information-faster-support/