Question: Is it possible to dig yourself out of a coffin?
Answer: Technically, yes. However, you'd have to be in a (rather flimsy) wooden coffin, which is unlikely, unless you live in the past; you'd have to punch your way out before running out of oxygen, which is also unlikely (even with years of martial arts training that specifically included how to punch a hole in wood at very close range); and you'd have to escape before the roughly 65 cubic feet of dirt on top of you poured into the coffin and suffocated you anyway. Finally, Beatrix definitely gets some help through editing, which you won't have.
Answer: Tarantino once explained to David Carradine that Budd was also in love with Beatrix. He left the DVAS right after the wedding massacre because he was upset he had to kill her.
Question: Why was Beatrix so shocked to hear Elle killed Pai Mei?
Answer: When Beatrix trained with Pai Mei we see that if you listen to him and respect him then he has a lot to teach. She wasn't so much shocked that Elle killed him...she is shocked at the lack of respect Elle showed in killing him.
Answer: She approached each foe in a manner appropriate to the situation. Budd was in a trailer surrounded by open land and total visibility, and he also knew she was coming, so sneaking up, quietly and unobtrusively, made sense. The real question is why, after taking so many precautions and being so quiet, she flung the door open and charged in as noisily and vulnerably as possible.