Lobo0705 is dead on, and here are the page quotes from the book to back him up:
QUOTE (Page 229)
As we’ve described, AR is normal living in physical space with an AR heads-up display. You can see the Matrix if you like, either by creating a virtual window or display screen and viewing it like a camera, or by overlaying device and host information on your normal vision. Your persona can go anywhere in the Matrix using this view. You can even enter hosts, although your icon will appear jerky and slow compared to a VR user in the same node.
QUOTE (Page 246)
The virtual space inside a host is separate from the outside grid. When you’re outside of a host, you can’t interact directly with icons inside it, although you can still send messages, make commcalls, and that sort of thing. Once you’re inside, you can see and interact with icons inside the host, but not outside (with the same caveat for messages, calls, etc.).
As for your follow up question, the entities in the host can't see the icons outside the host, and the entities outside the host can't see those inside. Therefore, the gunmen shooting at you and your troll friend don't see the IC closing in on you, and the IC doesn't see or care about the gunmen.