Questions about Turing Machine
We define the alphabet as the set of natural numbers.


No you don't. The alphabet must be finite.


  Am I correct in saying that, we do not know whether this Turing machine will halt for any given input?


If all you know is that the TM recognizes the language then you're correct: it could loop forever on some inputs.


  Since this is a decision problem, the language realised from it, will always b finite?


That doesn't follow from being a decision problem. This language is finite because there are only finitely many natural numbers less than 400. But, for example, the language of even numbers is infinite, but it's still a decision problem.


  Am I correct in saying that we have defined this Turing machine to accept one word at a time, where the words are numbers. We could have made it accept two words, if the algorithm was modified to accept two inputs.


Yes, you could produce a Turing machine that decides the language $\{x,y\mid x,y\leq 400\}$.


  How would the Language be for the problem: "Is X &lt;= Y?"


It would be the set of all strings with that property.


  For a decision problem, the elements in the Language realised are the solutions?


I'm not sure what you mean by "realised". (You wrote it before but the exact meaning wasn't so important, then.) A decision problem is any problem of the form "Does the input string have property X?" and it's naturally associated with the language of strings that do have that property.