1. Basically, the only thing you should be aware is that if your collector service is installed on a VM, make sure it is not high loaded as well as you've got the time being synchronized with the Host machine, this should be done to have all your graphics/trends undivided, however in case you see gaps in your graphics - check time synchronization or give more resources(CPU) to that VM. So its up to you where to install Veeam Monitor, almost all configurations are supported.
2. It doesn't really metter.
3. Actually, we haven't heard about any issues running database as well as the service on vCenter machine.
4. As soon as the collector gets all the historical data from vCenter, database will not grow so rapidly, so the database size depends on your infrastructure.
5. Make sure you're using the latest version available on our website, where we've reduced the load on tha database. Also please have a look this threadVeeam Monitor : Truly Enterprise-Scale (PROOF)