I probably have no advice to give, but I also would not try to follow the advice that was given. For example - why no vibrato - if vibrato gives a chance for the voice to relax? Trying to aim for exact pitch - how? Practice sight singing - how? Technique isn't there at all: how to use the body, breath, etc. In fact, I can imagine that trying to be totally precise in pitch could create some kind of strain. And then, how can the person tell whether they are on pitch? You can't hear what you can hear until you hear it.
What's wrong about "strain" and what's so great about "relaxation"? It seems to me these are mantras or hold-overs from thinking about keyboard technique.
Technical problems like breath, timbre, phrasing, and anatomical considerations should be addressed, but you also have to remember that the OP didn't present any information or indications as to his or her problems.
How can one tell when one is on pitch? Well, keyboards comprise a class of instruments that occasionally produce reference pitches. There are others, I've noticed. There's even a device called a "pitch pipe," I've heard.
"No vibrato," mirabile dictu, is a suggestion whose merit is easily clarified by observing the difference between someone who has adequate ear-training and is able to produce intervals at will versus someone who is deliberately blurring the vocal quality by modulating the frequency. It's an effective way of deliberately singing "off key." I hold that it should not be applied unless one is competent at producing accurate pitches.
I'd go on a site that is dedicated to singing. A piano forum is the wrong place.
That's not necessarily so.
I would try to pose some actual questions in an OP, however, rather than a laundry list of unreasonably vague demands. As though it were a ransom note.
I'd also begin with the songs of Webern, and the songs of Debussy, particularly those with text provided by Mallarmé. Or by imitating the song stylings of Lemmy Kilmister.
Topic: How to improve your singing style &voice quality