Is it normal for companies these days to solely rely on Amazon RDS backup without another backup strategy?

depends on actual requirements, but yes. Amazon's redundancy, segregation, and backup strategies are well thought out, and if you stick to a "well architected" design you can achieve very high levels of safety. AWS defines well architected in many tech docs and dashboards, and you can engage with their experts to achieve audit compliant redundancy and backup to suit almost any requirement.

no

When DB is RDS it is more convenient, why not? But, depending on needs, there could be databases not in RDS and you use traditional methods to backup them.