So should I always use "זה" and "זאת" instead of other pronouns? At the end of the "Basics" Lesson, under Grammatical Genders tips¬es they said "When using a third-person pronoun to replace a noun, the pronoun used is the pronoun of the corresponding grammatical gender," which is what made me think this should be יש לו or יש לה
Actually the word "זה" in Hebrew can mean three things in English: that, this or it.
I think that if you think of it as "that" or "this" it would make much more sense (since it rarely used as it).
So for example you could say: "זאת ילדה יפה" (this is a beautiful child) but you could also say "זה בית יפה" (it/this is a beautiful house)
I'm not sure it needs to be taken out, as this is the primary lesson on how to use יש and אין. But I think they need to do a lot better on explaining when to use זה and זאת versus other pronouns. Specific lessons on determiners and demonstrative pronouns aren't till much later in the course, and they need some better notes to go with these exercises to avoid a confusion that you can refer to any noun in any context with יש לזה
Those are two totally different letters that ended up being pronounced the same because of European influence. Same with tet and taw. Ayin (that first one) is supposed to sound... like... well... it was originally this funky throaty sound, (you can look up how to pronounce 'ayn in Arabic, a friend taught me) and same deal with tet (the first letter) which was originally like, a T but while pulling your tongue back.
Unfortunately, this means that there isn't a rule for how to tell which they're spelled with, just from memory. Unless you're like me and ended up learning Hebrew with an Arabic accent and actually pronounce them differently, (it was quite confusing when I tried speaking to an Israeli for the first time. Now I make a distinction between my accent in Classical Hebrew and my accent in Modern Hebrew). It was really odd at first, but it did help set the distinction in my head.
The word "wet" uses ט. You can remember that "מילים רטובות" (wet words) use ט. For example, drops, dripping, umbrella, and many others related to wetness use ט. There are more examples in this blog post: http://weepinggardenflower.tumblr.com/post/148788636808/%D7%9E%D7%99%D7%9C%D7%99%D7%9D-%D7%A8%D7%98%D7%95%D7%91%D7%95%D7%AA
It seems to act like א
Did you see the tips & hints for the very first lesson? https://www.duolingo.com/skill/he/Letters-1/tips-and-notes