It has to be "przez ciebie", using the emphatic version of the pronoun. "przez cię" just sounds totally strange to me.
Well, in every language you can observe the same preposition being used in totally different situations, Polish is no different.
"To przez ciebie" is mostly "It's your fault", if you want to say something positive it's rather "To dzięki tobie" (Dative) = It's thanks to you.
In English, "walking across" something typically means walking on top of it; you would "walk across a bridge" or "walk across the road". It would be a very unusual situation for someone to walk across a house (just how drunk are they?!), and you'd probably say instead that you "walked over it" or "walked on top of it". That would be "idę nad twój dom", I think?
"iść" happens right now (to be walking, to be going on foot), "chodzić" is general (to walk, to go on foot). So basically, Present Continuous vs Present Simple. Granted, so far you learned that PC/PS are the same in Polish, but Verbs of Motion are an exception.
An exception from this PC/PS distinction is where you are just 'walking around', without any purpose nor direction, then it's "chodzić" despite being Present Continuous.
It never does, unless TTS behaves weirdly (but in this case it seems okay to me). Ó actually sounds identical to U, and it's those letters that Polish people actually have difficulty telling apart (in which case knowing related words and different grammatical cases helps, because often a word with ó would have something similar that is spelled with o).