Henry II yes, Catherine no.
I don't know.
Sure, Catherine did not want a marriage between Mary and Charles in OTL but, if Mary is offered the throne of England, the situation is quite different and Catherine might see things differently. After all, in OTL, she wanted to have England as a ally, even proposing Elizabeth Tudor to marry one of her sons. She would probably be unpleased by the idea of Mary becoming queen of England as Philip's puppet.
Henry II still die during the tournament for Elisabeth’s wedding (the different name of the groom can not change things here)
Why?
Henry II's death is likely to be butterlied away by basically any POD taking place before it.
This death implies both Henry II and Montgomery launching their horses at the exact same speed, Montgomery rising his spear at the exact same height, Henry II having his head at the exact same place at the exact same time...
It is quite unlikely.
And even assuming it still occurs, Catherine might want to keep Mary in this ATL.
don Carlos married Elisabeth (as originally planned)
If Elisabeth marries Don Carlos as initially expected, that can have quite important consequences.
Don Carlos was heir apparent to the throne of Spain and heir presumptive to the throne of Portugal (coming even before Cardinal Henry).
Does he still die in the same obscure circumstances as in OTL?
Does he have children with Elisabeth? If so, are they successors to Sebastian I and later Philip II?