How segwit blocks are seen by segwit and non-segwit nodes? Let's say a miner mines a block.


In this block some transactions will be non-segwit and some will be segwit?
The block contains two parts:


The part with transactions
The segregated part with signatures of segwit transactions?

To old nodes non-segwit transactions look normal, and segwit transactions look like no-signature-needed valid transactions? These nodes don't see the segregated part containing signatures?
To new nodes non-segwit transactions look normal, and they recognize segwit transactions and check the segregated part to validate the signatures?
There aren't two part to a block like you describe. The word segregated in segwit means that the witness data isn't included in the TXID computation similar to how it always wasn't included in the signature hash computation. It's still included in transactions and blocks. 

With segwit, the signatures are in each transaction in a witness field that is included before the nlocktime field.

When a node relays a segwit using block to a peer that doesn't understand segwit, it strips the witness fields out of all the transactions that have them.  Since they don't have any rules pertaining to segwit data they're perfectly fine with this.

If you were to hand a stripped block to a non-outdated node, it would just drop it and ban you for giving it invalid data-- it knows about the segwit rules and attempts to validate the additional data.