Question: Once again I have some examples from a Death Note episode [10].

The main character says:

> 
> しかしおどろいたよ流河{りゅうが}。親睦{しんぼく}を深{ふか}める為{ため}に、突然{とつぜん}テニスなんて。[Note, Ryuuga is a character's name, the one he's speaking to here.]
> 
> 
> 

Later the same character, thinking to himself: 

> 
> アイツのこのテニスでプロファイルなんてするわけがない。
> 
> 
> 

I think I grasp the overall meaning of these sentences, but would like to understand how なんて operates in them and how it connects to the other verbs, specifically する and ある in the second quote and the omission of a verb in the second sentence of the first quote. I would also like to understand what なんて means generally, as dictionary entries haven't really helped me figure it out.

How I understand the quotes: 

> 
> 1. I was surprised, Ryuuga, that you asked me to play tennis so that we can get to know each other better.
> 2. He will not be able to profile me with this game of tennis!
> 
> 
>

Answer: 
なんて has two meanings in Japanese which function as two different parts of speech, 

1. to express surprise on the part on the speaker at some event that they are commenting on. This form usually occurs at the beginning of a sentence, but not always. Usually this is translated in the sense of "He's **so** fast", or "**What/such** a fast runner!".
2. to modify a phrase by giving it the sense of "like that...", or "such as...". The connotation is to diminish the significance of the preceding clause, or imbue a sense of vagueness. This meaning is derived from 等 [など]. Both of your examples fall into this category.

> 
> しかしおどろいたよ流河。親睦を深める為に、突然**テニスなんて**。  
> 
>  But I was surprised, Ryuuga. You suddenly asked me to play **tennis of all things** in order to deepen our friendship
> 
> 
> アイツのこのテニスでプロファイルなんてするわけがない。  
> 
>  There's no way he'll be able **to do something like profile** me by playing tennis like this.
> 
> 
>

It's hard to tell without context, but I assume/vaguely remember that Light was trying to figure out why L asked him to play tennis. Which is why he used なんて, in the sense of "if he's not profiling me, then what is his goal?"

Thanks to Chocolate for setting me straight on the two distinct uses of なんて.
I think in the examples you provided なんて is an expression of disbelief or surprise. It is another way to say なんと, which I believe you can find more easily in a dictionary.

So you could translate it this way...

> 
> しかしおどろいたよ流河。親睦を[深]{ふか}める[為]{ため}に、[突然]{とつぜん}テニスなんて。
> 
> 
> But I was surprised Ryuga; I can't believe (you would take up) tennis
>  to get closer to (me).
> 
> 
>