Is a tx in a block just displayed as a txid or is the whole tx displayed (like: decoderawtransction HEX)?
I think this has been elaborated sufficiently. Just want to add that the ordering of the transactions is also determined by the merkle root.
So why not just storing the txid, since the txid is stored in the mempool?
Is this just for security reasons in case someone hasn't a txid which is in a block but not in his mempool?
Mempool is just the intermediate holding space for transactions which have yet to be included in the block. Transactions are always removed when they are included in a block. The transactions are only concrete with the POW when a block has been mined which includes the transactions. If it doesn't get included in a block, then it won't be in the blockchain.
And when a node doesnt support segwit, how can he validate and accept a block when is bitcoin core version rejects the additional segwit block and the witness data is missing?
From my understanding, I consider older nodes which cannot validate Segwit transactions akin to an SPV wallet. They cannot validate that a segwit transaction is valid but they will always follow the longest POW chain difficulty-wise.