Perfect pitch is the ability to pull exact pitches from thin air. In other words the ability to hear a tone, and identify it as "A" or "G" OR to be able to sing an "A" or "G" with impecable accuracy without having to hear it given from an instrument (like a piano) first. Perfect pitch is generally thought to be a born trait. Often people with perfect pitch associate certain tones with a color or other description. Something like, "F" sounds red, or "B" is kind of fuzzy. They can actually hear the difference in the quality of the pitch. There are cases where some have claimed to "develop" perfect pitch, but many argue that they have in fact developed a good 'relative pitch.' With relative pitch, one has trained themselves to acurately identify one or a few pitches (often by the way it feels in their voice) and then are able to derive what pitch is being played by relating it back to the memorized pitch. So for example, a highly trained musician, with practice has a knack for always being able to sing an "A" on command. Then when an "E" is played, they can quickly recognize the pitch as being a fifth higher than "A" and correctly identify the pitch as "E." The best way to develop RELATIVE pitch, is to sing the same pitch often. Get an "A-440" tuning fork. Strike it and hum the pitch several times a day. After a while try to hum the pitch before striking the tuning fork and see if you have sung it correctly. Over time, you will develop a muscle memory in your vocal chords.
(I'm a voice teacher, so bear with me violinist)
VOCALLY, vibrato is the natural "tremble" or "vibration" in a singer's voice. This happens naturally when a singer is using good breath support. The pitch will "wobble" slightly. This tends to be a desirable sound with solo singing, as it warms the tone of the voice and give a fuller, richer sound. Often choral singers are asked to "straighten" a tone, or remove the vibrato in order to maximize blend within the large group. Everyone's vibrato is different and the varying pitches can get pretty muddy in a choral setting. Vibrato will come naturally with properly supported singing, and vocal maturity. Children do not have a natural vibrato. It is something that develops as a singer matures. Forcing a vibrato, by intensionally wobbling a tone can be damaging to your voice.
As I understand it, vibrato on a violin is the immitation of the natural vocal vibrato. This is a desirable sound to warm tone when playing the violin. I'm not a violin player, but I believe vibrato must be achieved by a physical wrist or hand movement. Surely, your orchestra teacher/and or private lessons instructor can help you develop this.
Hope I helped!
I'm a Vocal Music Teacher with a Bachelor and Master's degree in Music Education - Vocal emphasis