I know we have to make some mistakes, in order to learn, but the Hebrew course, is the only one in my courses that doesn't teach the word before correct us. There is no orange word with the meaning when you click it. And I know it's a beta version, but this needs to be improved. And I imagine that is a course for people who has a previous adknowledge of a language, like so many, that doesn't teach some rules, but is to hard sometimes without the help of orange words (the new ones). I did some lessons with a particular teacher, so I know the letters, but sometimes the sound of Duolingo pronounce differs from the sound I've learned, and that confuses me a lot. Thanks for this space.
When a language is alive it over goes these sorts of transformations. There are many examples around the world of spoken language dropping the more difficult parts. Specifically, when Hebrew was revived it happened together with Jews returning from exile and many different traditions on how Hebrew is pronounced came together.
I think both reasons created the "lax" version of Hebrew commonly spoken today.
Yes, it will be correct, since Hebrew doesn't have different tenses for the present, there's only one tense. So, it could mean both "the woman reads" / "the woman is reading", the meaning changes according to the context or additional words which tells the time/frequency of the action that's done.
I would say yes, it is a mistake writing yud there. Writing without nikkud is somewhat flexible, but writing with nikkud has very strict rules.
As for your other question - the ה doesn't get only patach, but also kamatz gadol or even segol - depending on several things: the first letter of the word it defines - whether it can receive dagesh, or not; also depends on the stress of the word it defines... so, it's rather a complex thing. However, the difference in pronunciation between patach and kamatz gadol is non-existing in Modern Hebrew, and putting segol is considered rather formal, so in colloquial language it's always "ha", or should I say "a" with a very faint "h". :)
If you wish, you can read some more about those rules here: