It's my typical philosophy, to let people dig themselves in their own grave and provide them the shovel instead of wasting time engaging in intellectual debates when people are not open to hearing your side of the argument. Why waste effort when no one's willing to listen right? But eventually, one needs to put the lid on the coffin...so here we go.
a. Pope Francis IS the Pope, yes, even if I'm not a fan of him
There are some thoughts here, and here on the topic
The fancy wording is in the articles above...I'll simplify it.
a. No person on earth has the right to judge the Pope
b. Sin is internal, not external, actions are external, intentions are internal
c. A bishop or Pope must be warned, they need to know what they're doing is wrong (by he competent authority)
d. A Pope does lose office when he becomes a manifest heretic, the Church (justice) would declare the Pope has lost his office. (Public office would require the faithful to know)
e. No, the sedevacantist position is not logical and can't be defended.
b. The NO is not Catholic..
Unfortunately, there are some that do not understand the theological diversity within the Church. The existence of the various missals in the Church do not make one less Catholic than the other. There are various theologies expressed in the various Liturgies in the Church. There is no theological supremacy of the Roman Rite to any of the others. The NO is a mixture of various theologies (Roman, Byzantine, Protestant) without a real focus, but that does NOT make the NO heretical or a danger to the Faith.
c. Unrelated to a & b
I do ask for prayers. There will be major things happening in September...