Hi Garacesh,
I should strongly recommend you contact us.
Your first issue mentioned from your IT Staff sounds like either a WebRTC configuration or Firewall/Filter/AV issue, which we can send you articles on how to resolve. Connections should be instant if you are on the same network as the devices you are viewing/controlling, as WebRTC will create a P2P connection over the Local network, this sounds like it isn't, and is instead going through the Relay. This can be confirmed in Thumbnail view, where a little yellow symbol appears in the bottom left corner that says "Indirect Slow Connection".
Your second question is also completely doable, we call it Dedicated Teacher PC and you can find the article for that on our Support page.
In the portal, if you use the little Live Chat symbol next to your email address in the top right, ask for me and we can arrange a session to go over everything.