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If the proposal doesn't pass by then (or is withdrawn) it fails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.
The european parliament can vote the bill down. But that's the last line of defense. The danger is that a lot of politicians will think that it's for the benefit of children (which is nonsense) and will therefore vote in favor of the law.
Right now it is actually the council of the EU that is preventing the law from progressing.
The "nearly powerless" refers to blocking the bill being the only thing the parliament is able to do. The commission can just keep proposing this bill, it only needs to pass the parliament once. Once passed, future parliaments are unable to amend or repeal the bill. The commission only has to win once, while the parliament has to block the bill every single time.
The commission isn't an extraneous entity, if the parliament and member states want a law or amendment the commission will write a proposal. It doesn't "have to" strictly speaking but it would.
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