Do you sign only the previous output of transaction? I need to confirm that I understand how transactions work in the Bitcoin network. Ok, so:

Alice is a network node. Alice wants to send bitcoins to someone in the network. Alice is creating a transaction using her wallet.
Every transaction has inputs and outputs. The inputs of every transaction are just references to some previous outputs of some other, older transactions that previously sent funds to Alice addresses.
To send bitcoins Alice needs to resolve the puzzle given in the scriptPubKey of a previous transaction's output by using her scriptSig which her wallet generates upon making a transaction. Basically Alice just needs to prove that she is in control of private key (related to address previous bitcoins were sent to) by signing the new transaction.



Did I get these steps right?
My confusion started when I was exploring the hash type because I saw many sentences that said the Output of a transaction is signed correctly. With my understanding (from above) I assume that the previous output is signed correctly? And therefor, an input of a new transaction is considered valid. But I couldn't find confirmation for this. Am I missing something? Thank you!
The sighash type conditions what is part of the digest which is eventually signed for the transaction to be valid.
Some sighash types allow to either include (commit to) part --or none-- of the outputs of the transaction in the digest. Using these far less common sighash types introduce some malleability for a transaction, which usually allow more flexibility when different parties create a single transaction.
You almost always want to use SIGHASH_ALL and you anyway should append a SIGHASH_ALL signature to an input before broadcasting a transaction.
Regarding your question and to sum up, you always sign the current transaction and append this signature to the witness or the scriptSig. This signature can be conditioned using different sighash types.
For reference, you can see the wiki page on OP_CHECKSIG (it only covers the legacy transaction format, though).