I'm very sure it is 'shake his head' and not 'shake his bead'. There is no such thing as shaking your bead.
To answer your second question, to 'see the last of someone' means that you are seeing them for the last time. You are correct, the speaker is thinking he will be happy to see the last of Ullman. The use of the word "won't" makes the sentence a bit more interesting to read. It makes it more amusing. It still is a positive sentence, even though the word "won't" is used.
If the sentence were, "Won't I be glad to see the last of him?", it would have meant that the speaker is questioning whether he'll be glad to see the last of Ullman or not.
But when you remove the question mark at the end, it becomes a statement, which is spoken in a different tone than a question. "Won't I be glad to see the last of him" implies that he is amused about the thought of being glad to see him going away.
If the sentence were "I won't be glad to see the last of him", it would have been a simple sentence meaning the speaker will be upset, but that is not the case here.
Another example of such usage: "One day, you'll be broke and begging in front of me, and at that time, won't you be sorry that you didn't accept the job I'm offering you right now."