On blockchain.info I saw a transaction labeled as "No inputs (newly generated coins)". Are these new coins generated from mining?
How come that such a transaction can have 30 confirmations, while others only have six confirmations?
No inputs means that the coins are coming from a coinbase transaction, that is, they were only moved "once", when they were created.
Transactions will have different numbers of confirmations based on how recently the funds were moved.
The issuance of credits into the Bitcoin ledger is done through (in finance terms) an issuance transaction. The Bitcoin protocol refers to this as a "coinbase". All issuance transactions are generated by "miners" (transaction processors) who are taking guesses at solving an impossible math problem. The winner who publishes the correct guess to the problem is given authority by the rest of the network to write this "coinbase" transaction into the ledger. Since it has no inputs (no sending account) it is this transaction that is the creation of credits in the ledger, and is an exception from all other transactions which must have inputs and signatures.
These issuance or "coinbase" transactions have confirmations the same as any other transaction, which is to say that the number of "confirmations" is equal to the number of blocks "mined" since that transaction was first published in the ledger.
Newly mined or generated coins are required to receive over 100 confirmations (I forget exactly how many) before they are recognized by the network. This is a safety factor to prevent Bitcoin 'counterfeiting' by a conspiracy of miners.