Did America bomb Al Jazeera a political opponent?

If the question is did American bombs hit Al Jazeera then yes but there's absolutely no proof that they were intentionally targeted, the bombs hit Al Jazeera in Baghdad in April of 2003 where if you remember the United States was conducting an invasion.

Now Al Jazeera a political opponent as you put it is allowed to operate in the United States and more than 50 % of the American people can receive news from Al Jazeera if they so wish to do so. https://en.wikipedia.org/wiki/Al_Jazeera_America

Comparatively Putin has put restrictive bans on foreign people operating in the Russian airwaves and foreigners are only allowed a 20 % stake in Russian media companies. Not that it matters much because Putin has installed anti-extremist laws that basically allow him to shut down any serious media outlet that threatens his version of the truth in Russia as you can see with the websites I listed above.

Back in America Rupert Murdoch is allowed to own Fox News a company that doesn't shirk on criticizing the administration and even allows RT to operate fully despite it being a channel that exists solely to spout out Russian propaganda. Can you imagine a government owned American media company operating in Russia that exists to do the same things as RT does here ?

Isn't American media influenced by government?

There are certainly government funded media stations but they still allow private media companies to broadcast nationally and they also allow RT and Al Jazeera to operate.

Look I get it you love Putin and it's cool to be anti-American but at some point you have to objectively acknowledge that the United States has better standards for freedom of speech and freedoms in general than Russia has. Will you at least admit that ?

The Press Freedom index ranks countries by how much freedom of speech they have annually and how much freedom the press has, it's conducted by reporters without borders. This will educate you https://en.wikipedia.org/wiki/Press_Freedom_Index