Yes, I'm leaning toward an inclined 6 on the first coin.
I've looked again at the third coin, comparing with the listing in Krause for Mustafa III and the Numista listing for Abdulhamid I at
https://en.numista.com/catalogue/pieces42262.html
Both coins are close, and the photos available are not great, but personally right now I'm thinking it's a better match for Mustafa III. You'll have to make the call, or perhaps someone else on this forum will be able to tell. In future if you have a possible attribution I recommend mentioning it in your first posting.
Yes, I think the dates on the second and third coins should be at the top. If you look at them carefully under magnification and varying lighting you may be able to read something.
Most likely the terms burbe and fals are interchangeable in this case.