Would love for some advice, people!
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Some more context:
I need to transfer a new clients wordpress site to a new webserver. So far, so good. The website is below 2GB in size and doesn’t have any fancy plugins what so ever.
I major problem to the wordpress site is though, a weekly occuring database error. Comes every friday *(“Error establishing a database connection”).* Another problem is the former admins won’t give away the SQL Database informations. The client want to move on from the former admins, as well as their webservers.
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For migration, it seems the WPvivid plugin is popular now. Here I have now two options:
1. **Migrate site with database:** I guess the error will plain and simple duplicate, or won’t it?
2. **Migrate site without database:** What would be the result? I guess a new, clean install of wordpress would create a new database! Good! But will a WPvivid Backup file still get me the old wordpress site to function? Would all *pages/posts/media/user/plugins* be here? Despite lacking the database?

You have to do #1 or you will lose all your content. All WP content is stored in the database.
However, that doesn’t mean the error will continue. It’s likely that error is caused by the current host, and migrating to a better environment will solve that issue.
You need the DB, it’s got all the content and settings.
Hire someone who knows how to migrate or get a managed hosting account with Pressable and their team will migrate it for you.
If you have access to the backend, and are able to use a migration plugin, what’s the issue?
The error may well likely have been that the site or db was hosted on a shared server, and wasn’t reachable at times.
You should be able to migrate the full site as it seems you are able to access the backend. You might need to be an Admin, if you aren’t already.
Check out the “WP Duplicate” plugin https://wordpress.org/plugins/local-sync . It is the simplest migration plugin out there. Just install the plugin on the source site and the destination site and click the button you do not need to enter the DB details.