Can two outputs from the same transaction be spent separately? I am reading the transaction part. I don't know how to get the transaction hash. Does the whole transaction (include its vins and vouts) get hashed?

If a transaction has two vouts (spent by different transaction tx2 and t3), when t2 and t3 spent the vout, they will get the same prevout hash. Is that correct? 

For example:

tx1:  tx1_out1  --------&gt; node_A ----tx2(using tx1_out1)---&gt; 
      tx1_out2  --------&gt; node_B ----tx3(using tx1_out2)---&gt;  


Will tx2 and tx3 have conflicts, since tx1_out1 and tx1_out2 are spending the same hash?
Short answer
Your questions, in order: Yes. Yes. No.
Long answer
When spending the output of a transaction, it is not enough to know the txid. You also need to know the index of the output. (In other words, whether it is the first, second, third, etc. output.)
The hash of the transaction you're spending and the index of the output you're spending is collectively known as an outpoint.
Quoting the Bitcoin wiki:

The OutPoint structure consists of the following fields:

Field Size: 32
Description: hash
Data Type: char[32]
The hash of the referenced transaction.
Field Size: 4 bytes
Description: index
Data Type: uint32_t
The index of the specific output in the transaction. The first output is 0, etc.


See also the bitcoin.org docs.