Do you think παρακολουθώ is related to ακολουθώ because you are following something with your eyes?

First of all, ο τοίχος is masculine and το τείχος is neutrum. Concerning the meaning, τοίχος is a wall of a building whereas τείχος is the defensive wall built around a city with towers, bastions etc. Τείχος is also used in the plural with this meaning πχ σινικό τείχος=Great Wall of china, μακρά τείχη= Long walls of Athens

I would like to know that too. Furthermore, what is the difference between κοιτάζω και κοιτάω

"see" when referring to vision is usually not used in the continuous tenses (is seeing, was seeing, will be seeing, etc.).

Compare:

"my son sees Julie" = he perceives her with his eyes

"my son is seeing Julie" = he goes out with her regularly on dates

I imagine that your son is not in a relationship with the wall :)