Can we say " The more tired you are, the more it's hard to concentrate" instead of "the more tired you are, the harder it is to concentrate" . and which of them could be more common? and also what about these to sentences? 1- The longer she had to wait, the more impatient she become. 2- The longer she had to wait, the more she become impatient.
As general rules, with many exceptions:
1/ monosyllabic words take 'er' for the comparative and 'est' for the superlative,
2/ disyllabic words ending in er, le, or ow, also take 'er' for the comparative and 'est' for the superlative,
3/ disyllabic words ending in y, take 'ier' for the comparative and 'iest' for the superlative, and
4/ most other words take use more for the comparative and most for the superlative.
I repeat that these 'rules' have many exceptions. Those exceptions simply need to be learnt by use. In fact, most English speakers do not even think about these rules, they just use comparatives and superlatives without giving any thought to the 'rules'. This may explain why some English speakers get them wrong, and why, as time passes, these 'rules' will become less and less useful.
In your case, 'tired' is disyllabic and ends in 'ed', so it uses 'more tired' for the comparative. 'Hard' is monosyllabic, so it uses 'harder' for the comparative. As a consequence, the correct usage is:
The more tired you are, the harder it is to concentrate.
Regarding your second sentence, either version is acceptable, however, you should use 'became' rather than 'become' as it is simple past tense. I personally prefer:
The longer she had to wait, the more impatient she became.
as the rhythm of the left hand side matches that of the right. Also it places 'more' immediately before impatient, which is the word that it is modifying.