Solutions that provide HA will serve you well - both a failover cluster instance or AOAG. Technet articles are great to help you with this and understand it deeper.
For instance, if you use a FCI (SQL Server failover cluster instance), while installing you provide a network name which identifies the instance. Your SSRS only needs to know this networkname\instancename. Then, when the primary node failsover, another node will assume the work and keep serving your SSRS with the databases. Do notice that this solution undergoes a small downtime - the time for the cluster to disconnect the disks from the prior primary node to the "new to be" primary node, while transfering the cluster groups.
If you use AOAG, your SSRS will have to work with the VNN (virtual network name), and, when a failover occurs, a secondary node will assume the work and keep providing data. As in this case the node has its own disks (providing a second copy of the data, while on FCI you just had one copy of the data), the failover doesn't face the "transfer the disks" downtime.
As for the report server itself, taking into account your comment, this pages will provide you great guidance to scale-out:
https://msdn.microsoft.com/en-us/library/bb522745.aspx
https://msdn.microsoft.com/en-us/library/ms159114.aspx
You may want to consider setting up a NLB to take advantage of having more than one SSRS server. This should be ocnfigured first, and you can read about it here:
https://msdn.microsoft.com/en-us/library/cc281307.aspx
And, just in case, some aditional information for Reporting Services with AlwaysOn Availability Groups:
https://msdn.microsoft.com/en-us/library/hh882437.aspx
(I don't have an SSRS server handy at the moment to test/confirm this, so I'm going a bit off-the-cuff here, and might not be 100% spot-on)
I've never had luck with using the ReportManager URLs when I want to pass in specific parameters. Try using the ReportServer URLs instead.
BOL gives this example format for passing dates using the ReportServer URLs:
http://myserver/ReportServer/Pages/ReportViewer.aspx?%2fProduct_and_Sales_Report_AdventureWorks&SellStartDate=7/1/2005
Best Answer
Best is to use Reporting Services Scripter
Kevin Kline highlights the functionality here and there is a good article by Dale Kelly for migrating reports using RSScripter at MSSQLTips.
Another way is to use the power of PowerShell. There are many script available like here and here.
There is other utility (which I have not used) called reportsync