Circled in red:
When I hover over it I get the message "8 active connections to the Bitcoin network". Should Is this number too low and how do I change it?
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That icon indicates the state of your connection with the rest of the Bitcoin network. "8 active connections" mean that you are connected to 8 other clients.
Since you got 3 of the 4 bars with 8 active connections, it is enough. As far as I remember, I always had 3 bars, so I guess it's the default setting. Probably, to get the last bar you will have to manually configure more nodes to connect with.
When you have 1 or 2 bars, there can possibly something wrong. Maybe your firewall blocks the port for Bitcoin (8333).
Under "settings" --> "advanced settings" --> "network" you can change the connection type from UpnP to static (UpnP is default). The static port can be defined in the "bitcoin.conf". Default port for static connection is 8333 if not differently defined in the bitcoin.conf.
In my personal setup i got a bitcoin node in a Virtualbox where the main machine connects through a VPN with all ports blocked. I have forwarded a random port on the VPN and activated UpnP on the bitcoin node, the node connects through the VPN with UpnP.
The other option for this scenario would be to forward port 8333 on all firewalls/switches or whatever port defined in bitcoin.conf .
Please take also into account that nodes need some time to connect. However, 8 connections should be fine for the average user.
Also to note, a running node is visible on the network, take blockchain.info connection log for example, an attacker could target, audit and exploit running nodes.