Learn English – most interesting or the most interesting

Most has two closely-related meanings.

1 the largest in number or amount
2 more than half / almost all of somebody/something

As that OALD link says, the most is often used for the first meaning - but informally, the is often omitted. It's never used with the second meaning.

Suppose The Queen of Hearts were to ask "Who ate my tarts?"...

A1: "The knave ate the most"
A2: "The knave ate most"

If several courtiers ate one tart each, but the knave ate two, then either answer could validly be given, since he ate more than anyone else (but note that A1 is a "very slightly formal" usage).

But if the knave actually ate more than half (but not all) of the tarts, only A2 is correct. Though the Queen might not understand that intended distinction, since the could be omitted anyway.

It's worth making the point that the is never included when most simply means very...

"I am most grateful for your help"

...but interestingly, whereas in...

"There were 50 people there, at [the] most"

... the is normally omitted, it's almost always included if we add very as an intensifier...

"There were 50 people there, at the very most"

Both sentences are correct, though I would favour the latter.

The first one requires a little more thought by the listener because, when parsing the sentence on-the-fly, the after the US clause changes Russia's position from first to second.

For the second sentence, the first part stands on its own:

Russia is the second most powerful country

and the after the US clause simply provides additional information (who is #1): it's an afterthought, and you could insert a comma to separate it from the main sentence.