who is Fonz? do you all like him?
this scene is from S5E3, the dotor delivering Pheobe’s triplets talks about Fonzie person all the time, others don’t know why, neirther do I.

Dr. Harad: Hi! Phoebe, I'm Dr. Harad, I'm going to be delivering your babies. I want you to know, you're gonna be in good hands. I've been doing this for a long time. And also, I love Fonzie. (Exits)
Chan: Did he just say, he loves Fonzie?
Mon: That's what it sounded like.
……

Dr. H: (entering) Okay! Let's see what we got here. Ohh, y'know, Fonzie dated triplets.
Chan: This Fonzie person you keep referring too, is that another doctor?
Dr. H: Oh no-no-no. Fonzie is the nickname of Arthur Fonzerelli. The Fonz.
(Dr. Harad exits.)
Frank: It's not that weird, is it?
Phoebe: It's very weird! I don't want some guy down there telling me, I'm y'know, 【【dilatedamundo】】!
Ross: To be fair, 【【he doesn’t seem to be impersonating Fonzie】】…
Phoebe: (interrupting) What are you doing?!! Why are you defending him?!
………

to be continuedcontinued from the above
………
[Scene: The delivery room, Dr. Harad is back and checking on Phoebe.]
Dr. H: All right, you're getting there. Oh, and y'know, these babies are very lucky.
Phoe: They are. Why?
Dr. H: They have the honor of being born on The Fonz's half-birthday.
Phoe: Happy birthday!
Dr. H: Just to clarify, 【【I'm not Fonzie.】】

………
[Scene: The delivery room, Rachel and Frank are there.]
Dr. Harad: (laughing) Oh Fonzie.
Rachel: Y'know who I always liked? Mork.
【(Dr. Harad drops what he's doing and stares at her.)
Phoebe: （to Rach）Undo it. Undo it. Undo it.
Dr. H: Fonzie met Mork. Mork froze Fonzie.
Rach: Yeah, but umm… Yes, but, Fonzie was already cool, so he wasn't hurt, right?
Dr. Ha: Yeah, that's right.】

my questions：
1. who is Fonzie? or “Arthur Fonzerelli. The Fonz.”
2. what’s so funny when Phoe says 【【dilatedamundo】】?
3. why Phoe thinks Ross is defending the doctor when Ross says 【【he doesn’t seem to be impersonating Fonzie】】.
4. why the doctor says 【I'm not Fonzie.】? we know he’s not Fonzie.
5. why is the doctor shocked at What Rach says? who is Mork? are Fonzie and Mork two enemies?

Question

who is Fonz? do you all like him?
this scene is from S5E3, the dotor delivering Pheobe’s triplets talks about Fonzie person all the time, others don’t know why, neirther do I.

Dr. Harad: Hi! Phoebe, I'm Dr. Harad, I'm going to be delivering your babies. I want you to know, you're gonna be in good hands. I've been doing this for a long time. And also, I love Fonzie. (Exits)
Chan: Did he just say, he loves Fonzie?
Mon: That's what it sounded like.
……

Dr. H: (entering) Okay! Let's see what we got here. Ohh, y'know, Fonzie dated triplets.
Chan: This Fonzie person you keep referring too, is that another doctor?
Dr. H: Oh no-no-no. Fonzie is the nickname of Arthur Fonzerelli. The Fonz.
 (Dr. Harad exits.)
Frank: It's not that weird, is it?
Phoebe: It's very weird! I don't want some guy down there telling me, I'm y'know, 【【dilatedamundo】】!
Ross: To be fair, 【【he doesn’t seem to be impersonating Fonzie】】…
Phoebe: (interrupting) What are you doing?!! Why are you defending him?! 
………

to be continuedcontinued from the above
………
[Scene: The delivery room, Dr. Harad is back and checking on Phoebe.]
Dr. H: All right, you're getting there. Oh, and y'know, these babies are very lucky.
Phoe: They are. Why?
Dr. H: They have the honor of being born on The Fonz's half-birthday.
Phoe: Happy birthday!
Dr. H: Just to clarify, 【【I'm not Fonzie.】】

………
[Scene: The delivery room, Rachel and Frank are there.]
Dr. Harad: (laughing) Oh Fonzie.
Rachel: Y'know who I always liked? Mork.
【(Dr. Harad drops what he's doing and stares at her.)
Phoebe: （to Rach）Undo it. Undo it. Undo it.
Dr. H: Fonzie met Mork. Mork froze Fonzie.
Rach: Yeah, but umm… Yes, but, Fonzie was already cool, so he wasn't hurt, right?
Dr. Ha: Yeah, that's right.】

my questions： 
1. who is Fonzie? or “Arthur Fonzerelli. The Fonz.”
2. what’s so funny when Phoe says 【【dilatedamundo】】?
3. why Phoe thinks Ross is defending the doctor when Ross says 【【he doesn’t seem to be impersonating Fonzie】】.
4. why the doctor says 【I'm not Fonzie.】?  we know he’s not Fonzie.
5. why is the doctor shocked at What Rach says? who is Mork? are Fonzie and Mork two enemies?

Answer

1.  There was a TV show called "Happy Days" and one of the main characters was "Fonzie."  Fonzie was a "cool" guy.  The tv show had been very popular in the 1970s (when the characters from Friends would have been kids.  They all would have watched the show).  They all would have known about the show and the character.  But it isn't the type of thing your medical doctor would talk about while you were having a baby.  It's weird.

Imagine your doctor started talking about how much he liked Joey from Friends.  Not just once, but over and over and over again.  It's weird.

2.  That's how Fonzie spoke.   (example: if your doctor said he loved Joey,  and you answered "How you doin'?")

3.  Fonzie spoke and acted in very specific ways and the doctor isn't doing that.  So Ross is pointing out that the doctor could be stranger than he is.  Phoebe doesn't want that pointed out.

4.  This is a little too hard to explain.

5.  Mork was from a show called "Mork and Mindy" (it was actually a spinoff from Happy Days - the character Mork first appeared on an episode of Happy days.  He was an alien from the planet Ork.  American television in the 1970s was strange).  Mork and Fonz had a fight - so if you really like Fonz, you would really hate the people that Fonz didn't like.  (but again, this is not normal behavior for a doctor.)

Answer

This is all about old American TV shows. 
1:Fonz is a character in Happy Days. 
2: Fonz spoke in a particularly exagerated way so I assume she imitates that.... dilatedamundo is not a natural thing to say.
3: When he points out that the doctor is not actually imitating Fonz that could be seen as defending the doctor. 
4:  He´s making a joke
5: Mork is from Mork and Mindy, another old TV show. I don´t know about a link between these two shows.