255.255.255 or /24 and 255.255.252 or /22 are not really subnets those are you masks.
so for example 192.168.3.0/24 is a subnet of 192.168.0.0/22
If you wanted to use the /22 space, then you could subnet that down to 4 /24's
If all your looking to do is get more address space - then you could change your current 192.168.1.0/24 to /23 and then you could use addresses of 192.168.0.1 to 192.168.1.254 were 0.0 would be wire and 1.255 would be broadcast.
I would look into that 188.8.131.52 thing though.. And sure looks like from your screen shot your switch has voice vlan support so you could put your phones on their own vlan different than your PCs and other devices.
This would limit your broadcasts to devices on the same vlan. But not really seeing that much broadcast there -- if your saying your having issues with the network maybe get a sniff while the issue(s) happen - maybe you are seeing a broadcast storm during that period?
But even a /23 should not cause you much issue with broadcast unless you have some really really chatty broadcast applications running.. I didn't see any real noise there like you saw in mine where browsers were broadcasting for espn.com, etc.
The dropbox stuff could be removed real easy - unless your using it for local sync between machines? Then your going to want to keep that on, if not turn it off - its a pretty chatty broadcaster.
And just for general tidiness I would disable PCs from being able to be master browsers - it can cause trouble with the browselist if you have machines that can be the browser and enter and leave the network often, they end up thinking they are the browse master and causing an election - it can mess with your browselist being up to date, etc. You really should turn that off on all but machines that are on your network 24/7 -- normally I would suggest you turn it off on all PCs!! And even on servers other than your DC(s) could turn it off as well. You only need 1 box on your network to maintain the browse list - and the DC should win the election anyway - so there is no real reason for other boxes to even participate in the process.
As to other broadcasters - I saw a few other ips running dropbox other than yours. And curious what that 184.108.40.206 thing is
Let me look up the mac if listed in your screenshot.