I would like to export my current existing reports / alerts for record and backup purpose, or maybe import to another new splunk system.
You are better of collecting them in something that is called an "App".
This is easily done in the Splunk-UI, "Apps-menu > Manage Apps > Create APP" . Give it a fitting name.
From the app menu you should now be able to find / see your app, go there and do your work inside this. Or move the already created reports, views etc into this new app. This is also easily done from within the Splunk-UI and accessible from the "Settings" menu.
This also makes it very easy to share the contents and or setup more detailed permissions on your work.
It also makes it super easy to distribute and to install the same app / content on any number of Splunk servers ... and if you create something awesome you can upload and share it in apps.splunk.com .
As already stated you can use the different API:s to access and list this information, however if you collect your creations within an app , it will be easily sharable , easily accessible and you can tighten permissions, deploy to whatever number of splunk servers you like.
All saved searches, and other knowledge objects are written to various .conf files in the $SPLUNK_HOME$/etc directory. This list of configuration files and Overview of configuration files may be of interest to you as a starting point.
Additionally there are some REST endpoints, such as /servicesNS/-/-/saved/searches, and /servicesNS/-/-/directory among others that you may be interested in invoking in a programmatic manner (or with the |rest command in splunkweb as well.