A large purpose of service oriented architecture is encapsulation. If no other microservices can make requests to your microservice, then you really haven’t encapsulated much.
If and when you need to support mobile devices independently of your web UI, you can have a mobile gateway. Same idea. This gateway is optimized to know how to handle mobile traffic realities like smaller download sizes, etc.
No, you definitely don't want microservices making synchronous requests to other microservices and depending on them that way.
But it still may be necessary for your services to depend on each other, and that's where you can allow that communication through asynchronous eventually consistent communication. Actor communications, queue submission/consumption, caching, etc.
Even in such cases you might want to move bulk of processing to asynchronous queue based system but part of the logic might need to be executed synchronously (authorise credit card payment, you can process the payment asynchronously later, perhaps in bulk cron jobs like Apple Itunes does it but initial authorisation which decides whether purchase is successful must be synchronous).