They have the power to send a proposed law back to the commission, to be revised. The commission has the power to send it back to parliament unrevised.
I think the Council of Ministers also comes into the process. The Council consists of the national government ministers whose purview includes the matter at hand; it's membership changes for each meeting. It's really just all the member governments of the EU, one nation one council-member.
No, once a proposal is made the commission can withdraw it but not amend it anymore
After the proposal is made parliament and the council shuttle back and forth (between each other) proposed changes for up to 3 times (I might be wrong on the exact number)
If the proposal doesn't pass by then (or is withdrawn) it fails
and to be clear - the Council of Ministers has primacy, the actual power in the EU, whereas the Commission is just the secretariat or Civil Service of the EU, they have no power to decide policy.
I think the Council of Ministers also comes into the process. The Council consists of the national government ministers whose purview includes the matter at hand; it's membership changes for each meeting. It's really just all the member governments of the EU, one nation one council-member.