First one is used when the person being spoken to (the your) is female. The second is for the gender being male. Mike is a male, therefore it is بَيْتَكَ. However, as an Arab, I would be more likely to say بَيْتُكَ. I don't know the grammar rules, but it seems Jackass318788 agrees with me.
hmmm it isnt consistent with Egyptian Arabic who would say 'beitak' and 'beitik' not 'baytak' or 'baytik'. Egyptians would also say 'kebeer' not 'kabeer'
This is some weird mishmash of MSA and Levantine that is painful to hear, no one speaks like this, no one writes like this. It is always either MSA or some specific dialect.
I'm not sure if the course contributors would have control over the font size, but if you want to report it you could perhaps follow the "general feedback about the course" advice here: https://support.duolingo.com/hc/en-us/articles/204752064-How-do-I-report-an-issue-with-the-course-