Hey @Sama_san,
Welcome to the community. I haven’t done the original ML course myself, so, I am not really familiar with the extent of over-lapping between the original course and the new specialization.
But if you feel that they have over-lapping content, then I think that you can easily complete the first course in a matter of days. This will also help you to revise your foundations, and if I am not wrong, Course 1 is filled with optional labs, something which was missing from the original course. Additionally, completing course 1 will help you to get up to speed with Python, since the original course was not served with Python.
For this, check out 03 of this thread.
As to this, it really depends on you how you want to proceed. If you want, you can go through some of the tutorials of these packages before you start with MLS, and it is most certainly going to help you. You can also start with MLS and check out these tutorials as and when you need them, and this strategy is perfectly fine as well. You will find that the MLS labs provide links to the documentation whenever a new function is used from these packages.
I hope this helps.
Cheers,
Elemento