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I implemented teleportation described on this page: Teleporation

Circuit diagram is as follows: enter image description here

since we use entanglement for teleportation, as entanglement is done before 1st barrier, just wanted to know after the entanglement/1st barrier: is Alice free to perform any operation on the circuit or the operations should be exactly what is shown in the above figure between 1st and 2nd barrier?

Also, can we apply 2nd H-gate prior to 2nd CNOT gate between 1st and 2nd barrier and still achieve teleportation?

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The circuit you've prepared will teleport an arbitrary $1$-qubit state from register $q_0$ to $q_2$. The operations between the first and second barrier are preparing a Bell measurement and so those should not be modified, while the operations before the first barrier are preparing a shared entangled state between Alice and Bob and so those do not need to be modified.

Otherwise you can apply whatever operations you like to $q_0$ anywhere before the first barrier, or anywhere after the second barrier but before the $CNOT (H\otimes I)$ that prepares the bell measurement.

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