Having more connections doesn't help with speed as much as reliability and security.
It is the ping that you should look at when you go to Debug Window->Help->Peers that can show you the quality of your connections.
You can always add more nodes as long as you are specific about which nodes you are adding.
Go to Debug Window->Help->Console and type "addnode <ip> add" to add a node with that IP address.
You can make these nodes add automatically when you start Bitcoin Core by adding a line (or multiple lines like it) to bitcoin.conf in your data directory.
addnode=<ip>
You can't really add more nodes. Bitcoin Core limits the outgoing connections to 8, unless you somehow modify the code and compile it yourself. You're correct about the last part however.
IMO, neither the number of peers nor the quality of peers is much of a concern. Bitcoin Core wouldn't connect to peers who won't relay blocks and the speed of the transfer is usually much slower than the validation speed. The validation speed is almost always the bottleneck. You would experience significant increase in speed if you increase your dbcache, if you have enough ram.