porting install scripts : can rpm replace apt?

rpm is mostly equivalent to dpkg, not apt; the apt equivalent is yum (on RHEL and CentOS up to release 7), or dnf (on Fedora, and RHEL and CentOS starting with release 8), or zypper (on SuSE). For your specific commands:

sudo dnf distro-sync
sudo dnf install jq
sudo dnf clean all
sudo dnf autoremove

or

sudo yum upgrade
sudo yum install jq
sudo yum clean all

(This works because jq is packaged under the same name in both cases. This isn’t always true; a given piece of software can be packaged under different names in different distributions or even different releases of a given distribution.)

See the Pacman Rosetta and the Ubuntu RHEL migration guide for details.

You might want to look into configuration management tools instead, they will help you abstract the differences away (or at least, deal with them more robustly).

Your if [ $(command -v yum) ] test is flawed because yum can be installed on Debian derivatives (including Ubuntu); its presence doesn’t mean it’s the package manager. You should probably detect the running operating system and base your choice on that; see How can I reliably get the operating system's name? for details.

No, the options and arguments to apt and yum are different, so are package names in a lot of cases.

You also seem to be getting rpm and yum confused, yum is the equivalent of apt, rpm is the equivalent of dpkg. dpkg is the backend for apt, rpm is the backend for yum.

You will have to look at the man pages for both apt and yum to find the equivalent options. Alternativly you could look at a configuration management tool like puppet which will abstract a lot of OS differences between distros, but this may be overkill for what you're doing.