Thank you very much for your question. As you say, Japanese children learn verbs quite different way. You can make TE-Form from dictionary form, of course. But I consider that it´s easier to learn from MASU-form for foreigners.
It´s because MASU FORM just without MASU is the root of each verb. For example, TABEMASU...the root is TABE.
One more reason is that in my youtube channel, I am uploading videos from the basic grammar and litle by little the level becomes higer.
Now I am teaching MINNA NO NIHONGO, Lesson 14, it means I haven´t explained Dictionary-form yet to my audience.
So in this video I conjugate TE form from the basic MASU form.
It makes sense, thank you. I also learned -masu form first. But I always conjugate from dictionary form. For example to go from MACHIMASU to MATTE just feels odd to me. I started a long time ago with a textbook called Japanese for Busy People which, in hindsight, was terrible. It used romaji exclusively.
How pity you already quit learning Japanese...But anyway I can say you can already speak and write quite good Japanese. The last sentences you wrote in Japanese here are really perfect