Some general points:
1) A lot of companies are offloading this kind of CRM to Salesforce.com - which provides a full range of connectivity solutions, including chatbots. I am not sure how easily the chatbots integrate with email or phone service, but it is a given that a chatbot can behave like a member of the conversation, by phone or email but especially as part of an instant messaging customer service. Salesforce.com is expensive.
2) [My opinion] There appear to be two kinds of chatbots discussed in this community: chatbots that provide entertainment and are able to respond by using “natural language processing” (NLP) and echo’ing input back as output. These can be fun but they are not good at extracting specific information from a user and taking action. By contrast, “Service” chatbots act on the users input using natural language understanding (NLU), and can be designed to automate parts of customer service (whether for task shortcuts, faq, or simulated conversations).
As far as I can tell most of the community of chatbot development is focused on entertainment bots. But things are changing, as the bigshot companies start trying to solve common problems (eg automating CRM). So you can try Amazon’s Alexa “skill” development; or you can try Microsoft LUIS “intent” analysis - both of which are available through easy to program inputting of canned catch phrases. Not too hard but it tends to force a chatbot conversation to allow limited variations on how people phrase things. If you like what you are getting, you can probably hire a consultant to connect this type of chatbot to email, phone, or instant messaging. You might go to Facebook’s chatbot developers group and ask the same questions there.
3) I believe user interface ideas are evolving from GUI (graphic user interface) into LUI (language user interface). Mobile apps do not have enough screen to waste on menus, buttons, and mouse movements. For those apps the the chatbot replaces the need for menus. In other words, the chatbot is the UI. I also believe that messaging will become the standard communication protocol used for deliver customer service and that service chatbots (even when they only do structured commands, like an old computer game).
This is hard stuff today. I thought I knew how to build service chatbots and I can hack one out. But it is going to be about a year before it becomes easy to toss off an FAQ that is genuinely conversational. Do it right or do it wrong, this is the future of premium customer service and it is obvious, when one tries to interact with a company’s customer service, that the industry has huge needs for improvement through automation.