No. US Steel is not the largest steel producer in the US. The steel market itself is fairly competitive overall so there is not really any company that has price setting power.
Businesses buy out other businesses across borders all the time. This is normal behaviour.
As for whether it's a good idea: in short, competitive markets tend to be a lot more efficient than protected markets - which ultimately leads to lower prices for consumers. Nippon Steel thinks it can operate US Steel more efficiently than the current owners and managers of US Steel, hence Nippon Steel thinking it is profitable for them to buy it at a price that is higher than what the current owners value it at (as reflected in US Steel's share price).
The fact that more efficient companies can buy out less efficient companies is an important part of what keeps market-based economies successful and dynamic. If you want to know what it looks like when economies don't allow this, take a look at the economic malaise in somewhere like Britain in the 1970s after several decades of protectionism and state support for failing industries (or if you take protectionism to a logical extreme, North Korea...)
There's potentially a line of argument about monopoly risk (monopolies are economically inefficient) but that seems limited here - US Steel is only the 24th largest steel producer and the combination of Nippon and US Steel will still be smaller than the biggest players in the steel market like Baowu and ArcelorMittal.
Depends on the country. Some are more protective of industries than others so they will block any foreign companies buying domestic ones.
Is it a good idea? The steel market is pretty competitive and US Steel is far from the leader in the market. They were a monopolistic power 120 years ago but they peaked over 100 years ago and have declined significantly since then.