Why some response type (i.e.list) in IG is not working?

The list response is not supported in Instagram. 

Please note different messaging platform supports different types of messages, you could refer to the Instagram documentation here for all supported response type.

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• Why the "quick replied" response on IG message can only shows on mobile app instead of web?

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• What message types are supported in Instagram?

  Please see the List of Supported Messages on Instagram below.

• Can we filter the list of member in Member? (i.e. by name/channel/tag)

  Yes, you can click the filter icon on the left. You can filter out specific groups of members by: Creation Date, Last Active Date, Channel, External ID, Name, Gender, Locale, or Tags. Please check the  reference documentation for more details.