CHAPTER 39:

"When I use the word "handicapped," my deaf friends get angry. Why is that?"

Before reading this chapter I am going to reflect on the previous chapter that I did read. This question goes back to the idea of being classified into these defined groups that only focus on one aspect of a person. Maybe this is what causes much of your friends anger.
According to American Heritage Dictionary, the word "handicap" has several meanings, but the definition that I will talk about is "a deficiency, especially an anatomical, physiological, or mental deficiency, that prevents or restricts normal achievement" (Moore, Lev. p. 249).
This definition alone could also be another reason as to why your friends get angry when the word is used. Although,  medically the definition classifies a deaf person as handicapped because it is a disability, and it is a disorder but because a deaf person  can not hear does not enable them from normal achievements  (besides hearing). 
I feel that because society is known for classifying groups of people with these names, deaf community may get more offended by which they are placed because they do not see themselves as handicapped.

"Every person, deaf, hearing, or whatever, is an individual. Let this not be forgotten. We need to get beyond the limitations imposed by labels" (p.251).

CHAPTER 38:

"Can 'Deaf' be used as a noun (as in 'the Deaf') or should it be used only as an adjective?"

I believe that classifying groups of people takes away from a persons individuality. For example, myself,  a hearing female ( a girl who can speak and hear without difficuilities) puts me into a group of thousands of other females who are not deaf. This classification leaves  every other aspect of characteristics that make up who I am individually somewhere off into the distance.
This exact feeling happens when deaf people are placed into a group (the deaf).
"Some deaf people object to the phrase 'the deaf'. They feel that it devalues the humanity of deaf people" (Moore, Levitan p. 246). There is no doubt that a person who is deaf is apart of the deaf community that live amongst us, but to refer  that group as "the deaf" can belittle many individuals that are in this classification.
A deaf person is an individual, just as a hearing person is. And, every person is entitled to their own sense of self, and I think it is important for society to recognize these characteristics in people and not classify them into these defined groups of people who all cant hear, (the deaf, the handicapped, etc).

CHAPTER 37:

"Is it OK to use the term "deaf-mute" in reference to a deaf person who can't talk?"

When I think about the word "mute" and read this question to myself the answer is obvious. Reading this question reminded me much of how I answered the question to Chapter 3, "Is there similiarities between Braille and ASL?"
Although to me the answer is obviously no, I dont understand how a person can relate the word "mute" to someone who is deaf  or even think that a deaf person automatically knows braille. These words are different within themselves and both have different meanings that do not involve deaf people.  "Mutism" is a medical or psychological condition- the inability or refusal to produce sounds (Moore, Levitan p. 213). Deaf people have vocal cords and voices just as the majority of hearing people do, but because they are deaf they can not hear their own voices. Speaking is not easy for a deaf person due to the inability to hear to produce words.
Before I was enrolled in ASL class I did not spend alot of time imagining what life would be like if you were not able to hear anything from the time you were born. Now that I have made it through ASL 1 and currently taking ASL 2 I have put myself in this situation very often to relate life as it would be to a person that is born deaf. As a child a hearing person learns how to speak by other people speaking to them. From birth a hearing person has more of an advantage of learning how to speak because they hear noises and eventually try to mock the person speaking to them. But, when a person is deaf I could only imagine how extremely difficult it would be to try and speak if you can not hear. 
If more people would put themselves in the shoes of a deaf person, these questions would become more obvious to many.

"Why isn't "deaf and dumb" an acceptable term?"

Well, read that slowly... "Deaf and dumb"
Just as a hearing person would get offended by the word "dumb" a deaf person has every right to get offended as well. If not more. Just because a person can not hear does not make them dumb by any means. In fact, ASL is a challenging language to become familiar with and many deaf people sign beautifully. Beyond that, deaf people have many disadvantages when it comes to adapting to todays world and it takes alot of practice and understanding for these individuals to learn how to communicate with others outside of the deaf community. To me, this is what makes ASL so beautiful. The deaf community deserve more than hearing people classifing them into groups. A deaf person is just deaf, still fully capable to do many of the things a hearing person can do without hearing!