As I understand, the Hyperledger composer environment runs on a Hyperledger Fabric v1.0 (or 0.8?) blockchain.
Beside the REST server to interact with the blockchain or see the transaction, participants etc. is is possible to see which transactions are in which block, like on the Hyperledger explorer? (https://github.com/hyperledger/blockchain-explorer)
Yes it is possible to see which transactions are in which block, and Yes you can use Explorer to view the transactions on a Hyperledger Fabric blockchain.
All you need is to clone the repo in the link you shared and create the relevant database by executing the mysql script mysql -u<username> -p < db/fabricexplorer.sql. Afterwards, you can start your network and note the channel name. Then, edit the file blockchain-explorer/config.json and include the channel in the channel list. Then, go to http://localhost:8080 and you will see the statistics of the channel you had indicated.
Hope this helps.