You cannot use FLOW3 packages in TYPO3.
AFAIK, TYPO3 does not yet have REST support, and it can be difficult to use RESTful methods like PUT or DELETE. However, you can use the usual Extbase ext and RealURL to create an API that can send responses for GET or POST requests.
BTW, if the only goal of your implementation is to create a RESTful API, I would suggest using a small framework on top of it. The main goal of TYPO3 is to provide a universal and convenient CMS system, but its performance can sometimes not be compared with dedicated solutions.
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