Alright, well it's costing me $4/month for ionos to register the domain.

That's top-end but not unheard of (for a .com). Given who ionos are (ie. the provider formerly known as 1and1) then that's outrageous and if I were you I would move. Just make sure that you haven't accidentally signed up for some additional thing which is where the money is really going. For comparison, $WORK provides .com registration and management for £25 p.a. (with a discount on that for multiple years and other bulk purchases) which equates to less than $3 a month at current rates and they are at the quality end of the market (eg. you can phone them up and talk to a technically competent person, etc.)

What are DNS zone settings?

They are referring to the zone data which is essentially your DNS records. This is reasonable in that if your DNS is up and running on some other provider there is no need for your previous provider to retain that. Do check that your new provider is actively serving the DNS and has all the data which from a cursory check appears currently not to be the case:

$ host -t soa merrillpjensen.com.
Host merrillpjensen.com not found: 2(SERVFAIL)
[download]

Do check that your new provider is actively serving the DNS

$ host -t soa www.merrillpjensen.com
www.merrillpjensen.com has SOA record ns1.digitalocean.com. hostmaster
+.www.merrillpjensen.com. 1600641995 10800 3600 604800 1800
$
[download]

$ ssh root@206.189.67.44
root@206.189.67.44's password: 
Welcome to Ubuntu 20.04.1 LTS (GNU/Linux 5.4.0-45-generic x86_64)

 * Documentation:  https://help.ubuntu.com
 * Management:     https://landscape.canonical.com
 * Support:        https://ubuntu.com/advantage

  System information as of Mon Sep 21 19:28:21 UTC 2020

  System load:           0.02
  Usage of /:            7.0% of 24.06GB
  Memory usage:          25%
  Swap usage:            0%
  Processes:             106
  Users logged in:       0
  IPv4 address for eth0: 206.189.67.44
  IPv4 address for eth0: 10.46.0.6
  IPv6 address for eth0: 2604:a880:2:d0::21c5:9001
  IPv4 address for eth1: 10.120.0.2

25 updates can be installed immediately.
0 of these updates are security updates.
To see these additional updates run: apt list --upgradable


*** System restart required ***
Last login: Mon Sep 21 00:18:51 2020 from 75.164.47.252
root@ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet:~# pwd
/root
root@ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet:~# cd ..
root@ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet:/# ls
bin   dev  home  lib32  libx32      media  opt   root  sbin  srv  tmp 
+ var
boot  etc  lib   lib64  lost+found  mnt    proc  run   snap  sys  usr
root@ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet:/# uname -r
5.4.0-45-generic
root@ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet:/# hostnamectl
   Static hostname: ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet
         Icon name: computer-vm
           Chassis: vm
        Machine ID: 9ad82a334ffc4f5a93859909d4e33b84
           Boot ID: 8b0de2dfd5864eb89bfd87db74b1f79e
    Virtualization: kvm
  Operating System: Ubuntu 20.04.1 LTS
            Kernel: Linux 5.4.0-45-generic
      Architecture: x86-64
root@ubuntu-s-1vcpu-1gb-sfo2-01-first-droplet:/#
[download]

Q1) How do I integrate the above domain into this filesystem?

Q2) (No question too stupid, right) If I'm loggged in as root, do I use sudo on my commands?

Q3) How do I keep tally and track of robots that want to knock on my door?

I always like the random art that comes with

$ ssh-keygen

+---[RSA 2048]----+
|+  .o.o          |
|.E.. = =         |
|. *...*.=        |
|.= o.oo*o.       |
|+ * . ooSo + .   |
|.+ +    . * o .  |
|o o .    o + =   |
| o   . .  . = .  |
|      . ....     |
+----[SHA256]-----+
[download]

Thanks again for comments. Again, I'm trying to get to the The Topic more squarely....

$ ssh root@206.189.67.44
root@206.189.67.44's password: 
Welcome to Ubuntu 20.04.1 LTS (GNU/Linux 5.4.0-45-generic x86_64)
[download]

That should not work. Really, disable root login, or at least setup public key authentication. You really, really, really don't want a password-based root login on anything reachable from the internet, not even when you use SSH. Generally, create an unprivileged user, make sure that user can use sudo (member of sudo or wheel group, depending on Linux distribution), and disable root login via ssh.

In /etc/ssh/sshd_config, set PasswordAuthentication no to completely disable login with passwords, and set PermitRootLogin no.

See also Greetings and salutations | sudo.

Q2) (No question too stupid, right) If I'm loggged in as root, do I use sudo on my commands?

Generally, you should not work as root, but instead use sudo. If you work as root, sudo is redundant, it just wastes CPU cycles.

Oh, and by the way: sudo su is still around in far too many HOWTOs. You do not need su at all, uninstall it. Use sudo -i if you insist on getting an interactive root shell. Use sudo -e somefile to edit a file as root.

Q3) How do I keep tally and track of robots that want to knock on my door?

Depends on your provider. The easiest way is to ignore them and let your provider deal with them.

Another quite easy way is to use fail2ban. It works especially well if your home (or office) uses a fixed IP address that is permanently whitelisted, that allows a very aggressive blacklisting of any system trying to access your server.

Alexander

--
Today I will gladly share my knowledge and experience, for there are no sweeter words than "I told you so". ;-)

https://www.digitalocean.com/community/tutorials has you covered on all aspects here. See also fail2ban. Setup ssh for keys only login, on a different port. They have tutorials on server hardening, hosting, you name it.