You can use it if you want to, there is no conflict between the two plugins. When Relevanssi is active, the results on the wordpress results page will be provided by Relevanssi.
If you prefer to use the search override feature, then you may disable it, so that the results from this plugin apply there. Otherwise it is completely fine.
We are not aware of any issues with Divi builder at the moment.
In terms of functionality, nothing at all. If you want automatic updates on the new site (and you had it active on the previous), then you can de-activate it on the old one, and activate it on the new. That is not mandatory either, as you can manually update anytime.