"này" is a demonstrative determiner. "nay" is a cognate word of "này", but it only implies the present time. "hôm nay" means today, "năm nay" this year, "ngày nay" nowadays. curiously enough, we would say "tuần này" and "tháng này", respectively this week and this month.
After listening to the audio a dozen times, I'm beginning to understand what AnCatDubh and MattJohnso293482 are saying. Just so you know, TranVanHaiNam and I can hear "thứ hai" very clearly. The issue here is understanding the difference between the letter "u" and the letter "ư".
The Vietnamese letter "u" makes an English "ooo" sound as in "shoe".
The letter "ư" makes a really weird sound. It's so hard to describe. To me, it kinda sounds like "uhh" and "luh" really blended together. Sorta how AnCatDubh described "thứ hai" as "tl hai".
Of course, we shouldn't forget that there's also a sharp or acute accent over top of "thứ" to indicate a "rising tone".
Anyway, the best way to distinguish between "u" and "ư" is to listen to them side-by-side. They are totally different. I just tried typing "u" and "ư" separately in Google Translate, and I think the audio there is decent enough for people to hear the difference. I hope that helps!
Năm = year/five but it depends on the context of the sentence. They are homonyms. Like in English we got "can". Ex. Can you open that can? Are you "able to" open that "tin container"? Does that make sense? However, nấm = mushroom and that word has a different spelling and sound. Hope that helps =)