Since this is an old posting, perhaps you already caught on to the difference: "ag glanadh" = cleaning but "a ghlanadh" is "to clean" and for good measure "á ghlanadh" is "cleaning it" while "á ghlanadh aige" is "being cleaned by him". It does take lots of examples and repetition which is why the advancement from level 3 to 4 requires about 27 sets of exercises. Bain sult as.
I gleaned these rules of thumb
infinitive: "tá orm mé [object] a ghlanadh",
'ing: tá mé ag glanadh [object] (object in the genetive)
'ing, object is a pronoun: tá mé á glanadh (cleaning it)
passive: tá sé á ghlanadh acu (it is being cleaned by them)
purpose: tá [object] le glanadh agam (there is an object to be cleaned by me, I have an object to clean)
Informed by these brilliant clips: https://youtu.be/xXquoFg8G38
There are a couple of mistakes in your rules of thumb that I thought I'd point out.
infinitive: the object always precedes the verbal noun, even when it's a pronoun e.g. é a ghlanadh and an carr a ghlanadh.
Additionally tá mé + infinitive is ungrammatical and doesn't mean anything. You could say tá mé chun an carr a ghlanadh or Tá orm an carr a ghlanadh but you always need a preposition.
You're missing a lenition in your passive example. Since the subject is masculine it should read tá sé á ghlanadh acu. If it were feminine it'd read tá sí á glánadh acu and if it were plural tá siad á nglanadh acu.
Hopefully that helps some. From what I watched of those videos it seems like the grammar's all correct and the explanations are solid.
The inconsistent grammatical rigor of these exercises drives me crazy. "He does not like cleaning his room" is marked as incorrect, while "He does not like to clean his room" is marked right. In English there is a subtle grammatic difference between the two, but they are colloquially equivalent. In other exercises, Duo has not seemed so rigorous and has accepted more colloquial translations.