After a few sessions of mindfulness meditation and concentrating on an eye between my two physical eyes, I started seeing orbs (of various colours and sizes), masses (coloured clouds or smoke), auras, and visual snow. Moreover, I noticed the frequency of psychic happenings increased dramatically and my ability to see what I visualize had increased.
My questions are:
Have any of you experienced or read anything close to what I am describing?
These types of experiences of orbs and other phenomena are not all that uncommon among meditators, and are a byproduct of the development of meditative composure (samādhi). The fact that you were specifically focusing on a "third eye" may or may not have contributed to the arising of these experiences.
What is Vajrayana's perspective on the third eye?
See the entry on Five Eyes
from Rigpa Wiki. This classification of five eyes is sūtrayāna, but in a nutshell, through developing perceptions of light (ālokasaṃjñā) one can eventually attain vision of the divine eye (divyacakṣu), whereby one can see beings from other realms, and so on. This is an advanced ability but is still considered mundane.
Does an opened third eye mean some kind of spiritual attainment? Or can someone on any level of spiritual development open it?
Some people are more prone to experiencing these kinds of extra-sensory phenomena than others. In the exoteric Buddhist teachings, light nimittas can be used to further develop samādhi or the divine eye, etc. They are neither good nor bad, and are not a sign of high attainments. For any practices that are not
exoteric, such as vajrayāna practices, one is best advised to find a qualified teacher and follow their advice.