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If the proposal doesn't pass by then (or is withdrawn) it fails
Right now it is actually the council of the EU that is preventing the law from progressing.
Framing it like you do is ignoring the fact that the only reason we're here in the first place is because a good chunk of member states and MEPs want this law