When it comes to privacy and security controls Signal and Telegram are my recommendations. As for the extracting features, I do not believe they will meet your requirements as the extraction goes against the privacy and security controls since i.e. I would not like the option that someone who I talked to on Telegram can just easily extract our conversation history to PDF and give it out somewhere. If you would like to have both then I would suggest using Protonmail, it is not as instant as IM but it has everything you need, privacy, security, and easy print option. https://protonmail.com/ Franklin Li
Signal would be my first choice for privacy and security.
You can't export conversations with IOS but with Android there is a way for syncing data with a new phone. Maybe you can find a way to work with that exporting file, if it's not encrypted (which I doubt). See here :