Hi Neeharika_Singh,
First of all, these questions are not related to Highcharts and frankly speaking go beyond the scope of our duty. I would suggest you asking on forums like
https://stackoverflow.com/. We are Highcharts developers and I think that in this case you should seek help from people who are fluent with networking topics. I will try to answer these questions anyway.
1) Depends where your machines are located. If they are within single LAN network, then you don't have to use internet. Otherwise, most likely you have to. Why? Because you need to transport your data between machines somehow.
2) Yes, your data is most likely 'exposed' to the internet, but in most cases it is secured by protocols like
HTTPS. As an alternative, depending on your setup, you could for example use LAN network, but I would highly recommend asking about it on stack overflow.
3) It looks like you use some sort of moment's
CDN, and without internet it won't work. If you want to use it without internet, then you need to install it locally.
4) No, your data is not being exposed, you actually download data, but those are moment errors, not Highcharts.
Regards!