During Thor's interrogation, Agent Coulson exits the room and Loki enters and informs him that his father Odin had passed away and that he cannot undo his banishment. Not only does he communicate with Thor, but he goes to the area where Mjölnir is embedded in the rock and attempts to lift it, with SHIELD scientists and agents completely oblivious to his presence. Loki shows a similar ability when he converses with 'The Other' and when he manipulates Erik Selvig. Is this apart of Loki's Illusion powers or another one of his abilities that has not been addressed?
Loki in the canon Marvel-Earth 616 possesses a wide array of both physical abilities and magical abilities which make him a force to be reckoned with in both Midgard and Asgard.
As far as him getting around Asgard and the Nine Realms without the Bifrost: He doesn't need it.
- The Realm Eternal has many places within it which offer transit to other realms within the Nine Realms. These act as portals between realms that do not require the Bifrost to utilize. They are hidden from most eyes and only due to his extensive travel of Asgard does Loki know of them.
Apocrypha (from old comic lore, now revised for the Marvel Cinematic Universe)
Early maps of Asgard showed the portals that connected its different realms as a single contiguous map with the Rainbow Bridge being the only permanent portal to Earth.
The Asgardian "supercontinent" was really a multi-dimensional land mass connected by portals allowing Asgardians (and visitors from other realms) to visit each other.
Epic tales described the relationships between the realms as able to be walked and groups met, waged war, treated and traded. Young Thor and Loki adventured in all of these places traveling solely by horse (and portal)
As far as his telepathic and many magical abilities:
- He possesses the power to project his mind across any number of the Nine Worlds and communicate telepathically with his vassals or even minds not associated with his own.
Psionics: Loki has demonstrated powerful psionic capabilities, the full limits of which aren't known. He has demonstrated the ability to project his thoughts telepathically across great distances as well as potent hypnotic capabilities. He is able to communicate with beings telepathically, though his ability to do so is greater with beings that serve him.
- As a sorcerer of the first order, he is also capable of astral projection, which allows him to separate his body from his spirit and travel the astral planes which connect all of the Nine Realms together.
Astral projection (or astral travel) is a paranormal interpretation of an out-of-body experience achieved either awake or via lucid dreaming or deep meditation. The concept of astral projection assumes the existence of another body, separate from the physical body and capable of traveling to non-physical planes of existence. Commonly such planes are called astral, etheric, or spiritual. Astral projection is often experienced as the spirit or astral body leaving the physical body to travel in the spirit world or astral plane. Often used as a form of telepathic ability or magic power.
Loki in the Cinematic Universe
In the Marvel Cinematic Universe, Loki appears to possess similar physical durability, mental capabilities and magical prowess as his canon comic counterpart.
It's revealed in Thor 2 that Loki maintains a number of "back doors" into other realms so that he doesn't have to rely on the Bifrost to cross between worlds. This accounts for his physical travel, but the last two examples you list appear to be some form of astral projection allowing him to communicate across great distances without physically being there.