Is this a school exercise? This goals seems an artificial goal to exercise ARI, rather than a useful business goal.
Asterisk is a toolkit. It doesn’t have standard patterns for high level operations. The pattern you are using creates a channel to an end point, then runs a section of dialplan on that channel. You have to supply it with dialplan that does what is necessary to complete the operation. In this case, the dialplan should closely match the typical beginners; examples for making outgoing calls, but it still has to exist.
There are three types of number in your examples. In the first example external number represent digits to dial, and internal number represents the name of an extension in the dialplan. In the second, internal number represents the name of a peer definition, in sip.conf, and external number is the name of an extension in the dialplan.
Before you start using new features, like ARI, you really need to be comfortable that you understand how to configure a simple PABX, using just dialplan, and that you understand what the configuration means.
Also note that chan_sip is scheduled for removal from Asterisk in the near future. You should use chan_pjsip for new SIP based systems.
If your real gaol is click to call, there are many examples around, although most, or all, pre-date ARI.