Yeah, i can offer up solid suggestions, but i need to know more information about your network, so i can tell you WHAT EXACTLY to check, and where.
It would be PARAMOUNT that atleast a basic Network Map be provided to me.
I realize that it is ONLY the printer that you are needing to connect.....but since you did MANY troubleshooting steps already, I need to look and ponder over the network.
Honestly i think its just a matter of getting the printer an IP address, allowing it to communicate with your macbook pro (and all the other computers on the same network)
Normally, the printer will announce it self to the network (once you power it on, and connect it to the network with a cable, but wireless can be a bit more tricky and have MORE dependencies, than just using a network cable.
I see you mentioning that you are connecting the printer to the network over the WiFi, but printer will not connect after 3-4 times.
Are you saying....that when you try to connect the printer to the WiFi SSID with the password (or maybe your network is open, requiring no password, just the SSID) that the prinetr DOES connect, but only stays connected for a brief moment, then drops....and after repeating this process 3-4 times...the printer just wont join at all, not even for a brief moment?
are you saying that the printer simply will not join the WiFi network, and you basically give up trying after 3-4 try's?
The factory defaults for the printer are important, when you are trying to connect over WiFi, as some settings are already setup in the printer. Like the default IP address, and the timeouts for a DHCP server to answer to give the printer an IP address on the network.
It gets even more complicated if you are using VLAN's and multiple subnetworks....but that would lead me back to needing to know how your network is setup.
I understand your concerns about the security issue of me being on your network.....but I wouldn't be a very good technician, and would have been fired LONG AGO, if I was doing nefarious things to my customers networks, and their computers. This is my livelihood, how i pay my rent......I would not do such a trivial thing to a complete stranger, with little to nothing to gain, but a LOT to lose.
I have been working in IT since 2011, and have a college degree in Computer Networking. Ive done Many Remote sessions over the years, and have MANY customers vouch for my professionalism....if you would like a few previous customer referels, if that would set your mind at a bit more ease.
But there are SO MANY different possibilities that COULD be an issue.....that I could easily spot....if i was on the network able to make network queries.
It really would benefit not just YOU, but it would allow me to help MORE people, as I can get your issue resolved faster on a REMOTE SESSION, rather than a lengthy Q and A session with long periods of time where you would need to execute the queries and commands I would give you, and then report back the results.
Rinse and repeat....until the issue is resolved......could take hours....days even.
So wont you kindly reconsider having a REMOTE SESSION?