No, by far not every SNP has a RS number. Only those submitted to dbSNP are listed. These are either SNPs picked up during the larger sequencing efforts such as 1000Genomes project or TOPMED or SNPs that individual researchers probably found "useful-enough" in their work to submit to the database. Still, a SNP listed in dbSNP does not imply it is important or meaningful, same for SNPs being absent.
That might be correct, only known SNPs get a number. If your SNP becomes 'known' (thru publication) it will probably get a number.