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Given whole bunch of political deadlocks and big number of non-aligned voters third US party would be good solution of many US problems.
Why there is no even slightest sign of forming such third major political party in USA?
I heard somewhere that there is some law related to government formation which prevents that. Is that true?
There is no law preventing the formation of additional parties in the United States. In fact, we have a number of alternate parties, including the Green Party, American Independent Party, and Libertarian Party. However, these parties see few to no electoral victories.
That said, there is very little possibility of a third party viable in the long term. That is because the United States elects its representatives through a plurality ("first-past-the-post") voting system. In the United States, each state is divided into separate districts (the number of districts being roughly proportional to the state's population), and in each district, the candidate who gets the most votes, wins. This system will always trend towards a two-party system.
If you want a legislative body with multiple parties, you need to have proportional representation. There are a number of proportional voting systems, but in general, they let each voter select a party, the party has an ordered list of candidates, and each party is allocated seats to assign to their candidates in proportion to the number of votes the party received. There are some systems that also let you vote for individual candidates as well, but all of these systems allow for a number of parties.
For an accessible illustration of the way various voting systems work (including their effects on the number of parties), I strongly recommend CGP Grey's videos on the subject. They're only a few minutes long a piece, and are definitely worth watching.
