BM sent Cracker after Luffy after hearing he beat Doflamingo.
No, Big Mom implied that Luffy will get past Cracker. And she sent him because there was no one stronger available at this point.
He would have beaten him if not for Nami so she was correct in her assessment that 1v1 he would have won.
No, Luffy would've won. Luffy is known for being goofy and taking a beating from weaker characters before overwhelming them. He beat Crocodile and Enel but yet against Foxy, he had an extreme diff fight. Match ups matter too.
And last time I checked, Cracker had an obese base Luffy before himself who could barely move or breath and was complaining, saying he gonna report to his Mommy that King Baum helped them.
Joker > King > Queen > Jack is literally the theme here.