i see many connections like when I use netstat, are they all to the internet?
That depends on the output, you have to tell IPv6 and IPv4 apart. In IPv4, the following adresses are so-called private:
172.16.0.0 - 172.31.255.255
192.168.0.0 - 192.168.255.255
and are there any connections to the internet or other things that aren't forthcoming?
netstat lists all open connections, so the answer is no.
I guess what i'm asking is what does "AC adapt4r is online" actually mean?
Did you mistype that? An "AC adaptor" is the thing that plugs into a wall outlet and powers your computer. "AC adapter is online" means that your computer is currently on AC power (as opposed to battery power).
and do I have to have a wifi adapter to connect to the "cloud" or is there something builgt in that does that without my permission?
The "cloud" is usually used as a modern-day buzzword for what the elders call "server" (I know I'm generalizing). That server (or cloud, if you wish) can be either "on premise", that is in your home or company, or it can be "in the internet". Either way, your computer can only connect to other computers through network interfaces like wifi and ethernet. The cloud is not something that is built into the hardware.
If you have a network connection and do not trust your computer, then you need to learn about networking, routing and firewalls to stop your machine(s) from making potentially unwanted connections.