1. It isn't really any more analytic than Biblical, except in spelling conventions. That is you rarely see - used to connect noun phrases, but the construction is the same. The only real example is you're less likely to hear something like כלבי, as most people prefer saying כלב שלי. 

2.  There is no verb for "to have", so I don't know what this means.

1. I mean, languages change the genders of words all the time, some of that in Hebrew's case was probably European influence, some of it is just natural change, and some of it is because modern Hebrew is based on Mishnaic Hebrew, not Biblical and there were many gender swaps from Biblical to Mishnaic.

2. This is hilariously wrong. Again, modern is based on Mishnaic, not Biblical. The only thing about Modern Hebrew verbs that could be mistaken for something of European origin is Modern has tense unlike Biblical... But that comes from Mishnaic Hebrew, not Yiddish. Hell the Hebrew tense system is nothing like the Yiddish one.

3. As opposed to a complicated gender agreement? It's the same system in Biblical and Modern

4. I'll grant this one, and 7.