Can I take the finished product and take it to another cloud platform and host it there ?
(Do I need to pay Mendix for hosting the backend of my application no matter what )
Answer: Yes, you can take it to other cloud platform, however, you still need to pay Mendix license fee (not the hosting fee)
There always seems to be this mx logo from Mendix in the upper left corner of the Application.
Can I change the application so, that there is no mentioning of Mendix and it doesn't look like it's related to Mendix ?
Answer: You can change the logo from Studio (not Studio Pro). When you open the App in Studio, there will be a paintbrush icon on the left (Styling Menu), you can go there and change the logo
It seems as you need a license to implement Databases, but can I later host my own Database or do I need to pay Mendix for hosting the Database for me?
Answer: You can connect Mendix App to your database, but, regarding Pricing, you will need to discuss with Mendix Sales team. I understand there are flexible license fee options available now.
Is there something else I should know regarding this topic about to the Mendix platform ?
Answer: I am sure there are a lot of things you would need to consider like the number of users, application availability, backups, collaborative development etc. Mendix Sales team would advise you appropriately
Regarding Ready Applications, there are tons of them on the Market place. For example you can find financial applications at https://marketplace.mendix.com/link/industry/FinancialServices