Should we use a separated database for our data set?
Talk to your hosting provider. If they can't answer these questions, get a new hosting provider.

These really are concerns you should bring to your hosting provider. A quality hosting provider will be able to meet these needs and tailor a solution that ensures smooth operation of a site as a whole and within the individual components: Solr, MySQL, Apache/Nginx/Litespeed/etc.

How will they do this?


Benchmarking - Before launch, they'll launch a version of the site and then work to ensure that certain performance criteria are met. They'll tweak and scale to meet these numbers.
Infrastructure - Just having a master/slave DB isn't necessarily a solution. You have to have good infrastructure and equipment backing it up. It also has to be architected well. Good providers will have this.
Multiple Layers of Scalability - Having multiple strategies to handle load or large sites is key. This means not just having a huge DB but also effective content distribution (CDN) and internal Drupal caching (Redis) in addition to strong infrastructure.