Let's go for your last question first.
The short answer is no it isn't feasible to try and develop a "killer" vaccine that could target all likely mutations before they occur. But the good news is that such a single vaccine isn't needed.
A better way to accomplish this has already been in mind among vaccine scientists for a while. Anthony Fauci recently spoke about it.
- Keep the original vaccines directed against the entire sequence of the Spike protein gene, as it was known a year ago in January 2020. Use these vaccines as the primary vaccinations.
- Keep up with the various Spike protein mutations as they appear in new strains of the virus.
- Edit the sequence of the Spike protein gene to reflect the new mutations in either the mRNA vaccines (Pfizer or Moderna) or the recombinant DNA adenovirus vaccines (AstraZeneca, J&J, or Sputinik).
- Use these edited vaccines as booster shots for those already immunized with original vaccines directed against the January 2020 version of the Spike protein gene. That should get the job done. And it would be much easier to accomplish that than trying to develop the One Vaccine That Rules All Spike Protein Mutations.
I'll attempt to answer your broader question, but I first must know how much chemistry you know, the basic high school kind of inorganic chemistry. Next, are you familiar at all with college level organic chemistry? And similarly, what do you know, if anything, about protein 3-dimensional structure & chemistry. I find it hard to talk about immunology without also talking about protein structure. So, I have to know what you know and what you don't know.
Proteins are very large organic molecules, with numerous chemical properties. They are so large that it takes single genes, large amounts of DNA sequence, to provide a blueprint of their amino acid sequence. If it helps, we can consider the DNA sequence of a protein as a simple linear message that describes what amino acids must be assembled in what linear order to make the protein – it has a single dimension. Once made, the protein assumes a large 3-dimensional physical structure determined entirely by it's sequence of amino acids. It also has the important chemical features of numerous positive, negative, or neutral charges across it's surface, as well as numerous ways it can interact with the surrounding molecules of water or grease (phospholipids in biological membranes).
Audio can be a useful analogy: Musical signals consist of a complex mix of varying voltages. Once these multiple one-dimensional signals (DNA gene sequences) are amplified (mRNA copies) and sent to loud speakers (translated into proteins) that one-dimensional varying voltage becomes a large complex, 3-dimensional sound pressure wave that expands with time in a roughly spherical pattern.
That's the starting point. It quickly gets more complex from there.