"I open the window."
Maybe you are talking about the imperative mood, when we ask someone to (open the window). This is the not the case here.
Imperative: Open the window: افتح الشباك (iftaH aš-šubbák). Imperative to singular masculine.
Statement: I open the window: أفتحُ الشباك (AftaHu aš-šubbák) or more like (aftaHuššubbák - phonetic approximation). Notice the Hamza on Alif in the beginning - this one does not exist in the imperative mode. This Hamza (or Alif-Hamza or Hamzat QaT3 همزة قطع) is like a prefix for (I -Verb-), so no need to add أنا (aná: I, I am) to the statement (unless maybe for emphasis of some sort).
I guess you mean أفتح. Yes, that would be the verb. The sentence would be something like: إنني أفتح النافذة or إنني أفتح الشباك. The word إنني (2innanee) means (indeed I am) or (verily I am); There is no word-to-word equivalent for it in English but it is a particle used for emphasis and as I've done some translations from time to time I've noticed that using this with the present tense in Arabic is somewhat equivalent (somewhat, not all the time) to the present continuous. So, إنني أفتح الشباك would be (i am opening the window).
Yes indeed. I would use إنّني + أفتحُ الشباك; Altogether: إنني أفتح الشباك.
Innanee إنّني breaks down to: إنَّ (2inna) and the suffix ـني (nee).
The particle إنّ is typically used in emphatic sense and as you have seen already it helps on approximating the idea of continuity of the verb. In Quran translations, this particle can be found translated in various ways depending on the context; Once as "verily" and once as "indeed" or sometimes even as "Lo!" if I remember correctly.
The suffix ـني (nee) is just the personal accusative (me) attached. Thus, the whole meaning turns something like (I am indeed), or (I am doing).