That's not correct. See 'second best'.
That's just not true. If the US government doesn't set tariffs then all the gains from trade on the US side go to the US traders. Since these people also set the price they will set it so as to maximise gains to (themselves and therefore) the US. So a US tariff can only hurt the US as a whole. This argument applies whether or not China has tariffs.
Only if we consider the first order effects -- and only if we consider them simplistically as mere consumers.
Because the wider view is that those "consumers", are also workers, and the "race to the bottom" effect of modern global trade with the developing world hurts their bottom line, and leaves them without money to be consumers anyway.
The US, and other western countries, have used tariffs to great effect throughout their capitalistic development.
2 there are arguments that, in certain, very special conditions, optimal for a single country to have no tariffs even if others do
3 more generally one cannot say - this is called argument of second best - and adding a tariff may make situation better not worse