Did people pay respects to the dead as they do now after mummies were buried? Also, was everybody mummified?
Yes, people paid respects to the dead with some similarities and some differences to modern Western practices. No, not everyone was mummified.
A major function of an ancient Egyptian tomb was to provide a place for people to continually bring offerings and prayers for the deceased. We know that people did actually perform these tasks based on graffiti that some visitors left behind in antiquity! You can see examples of this kind of graffiti on the Reliefs from the Tomb of Nespeqashuty. It was considered a pious act to leave your mark!
Graffiti is necessary! Were the people not mummified considered "not worthy" or something? Or did they not have any money to pay for the mummification process?
You're right, it was a matter of money. People belonging to the middle to upper middle class and above could afford a mummification and burial of varying elaborate-ness. The lower classes would be buried in the sand with a few grave goods. Most of what you see in our galleries are very fine examples of ancient Egyptian material culture representing the most wealthy individuals.
Why are there chisel marks in this piece?
We're not sure exactly when those chisel marks got there. When these blocks were excavated in 1923, the excavator noted that the reliefs had already fallen off the walls of the tomb so he didn't chisel them off!