In old UNA versions there was a limit on the number of modules which can be requested for an update at once, this is the reason Updates and Purchases pages was giving an error, since you have a lot of modules installed. I've temporarily changed some settings on una.io server to allow bigger GET requests. We've fixed it in later UNA versions, so once you are updated you shouldn't have such problem, despite the una.io server settings.

Also I've noticed that UNA cron on your server is running once in an half an hour, however it's recommended to run it every minute. It may lead to the longer delays when update is requested and some UNA internal cron jobs couldn't be run at all.

Now you can proceed with further updates.