You can allow Java, as it is trying to search for updates.
These updates for Java will correct possible bugs and exploits in the software.
As for the prevalence reporter:
What is Prevalence Reporter?
My firewall warns: "Prevalence Reporter is trying to access the Internet" - what is Prevalence Reporter?
Prevalence Reporter, which has the file name ‘avgcmgr.exe’, is a legitimate part of an application in the anti-virus program AVG 8.0. It lets you know about potentially malicious and dangerous sites on the internet.
Your firewall may bring up a message when you connect to the internet that states: "Prevalence Reporter is trying to access the Internet"
Allowing Prevalence Reporter to run on your PC will mean that your web searches will be accompanied by a green or grey check mark next to them.
A green site is safe, while a grey site could be dangerous. You then need to make a decision about the site you are trying to access – continue to visit it, or take AVG’s advice and leave it alone.
You can place your mouse over the check to open a small box containing information about the search result.
It’s perfectly safe to run Prevalence Reporter, but it won’t harm AVG 8.0 if you don’t.
According to AVG, there are certain processes and URLs that need to be allowed in third party firewalls or software that checks network traffic, such as content filters or parental control, in order for them to work properly.