I was looking at my network shield, and I noticed some weird entries from things like digicert, safebeta.cn, edisk.fandm.edu, but none of them were listed as dangerous or suspicious
Not sure where in the network shield you were looking, my guess is that this was just the Real-Time Shields, Protection Status wheel showing files/locations scanned, etc. or the Real-Time Shields, Network Shield and the stats at the bottom of the page ‘Last analysed connection’ ?
In any case the network shield checks connections against its known malicious sites list, if a connection is going to one of those it will alert and block access to the malicious site. During your browsing many hundreds/thousands of connections to sites will be made and will be checked against the list.
A single page can have many connections to third party sites (images, adverts, some content, etc.) and these are checked also.
It was the last connected on the Network Shield. Some of them showed DNS in front
So nothing to fear? I run NoScript, so there banner ads that are called up that are not shown. Are you saying that is where these connections are coming from?
DNS being in front isn’t a problem as the intent is that something wants to connect to a web page, etc. but they just have a domain name (e.g. example.com) to be able to connect to that domain it requires an IP address, this information is obtained from a DNS server (Domain Name Server). Avast’s Network Shield can check if the domain is on the list.
Nothing to worry about.
NoScript as far as I’m aware doesn’t have any gripe with (or even check) banner ads as they aren’t scripts, the banner ads/images, etc. are just examples of things that the Network Shield would check the domain isn’t considered malicious.