BIG NOTE: Mages and Clerics get Mana from INT and PER so keep that in mind when consider trait allotment.
It's difficult to answer that question without giving away spoilers. The Wiki has a
a list of trait checks in the game if you really want to know exact details.
In general, yes, there are several places in the game where passing an INT, AWA, or PER trait check will make a difference in the game. The so-called "peaceful" ending of the game can only re reached by passing a high level trait check of several traits.
In general, yes, there's a difference between INT, AWA and PER trait checks. The ability to translate something, for example, requires an INT check. AWA is required to spot a few secret levers in the game. PERS is required to win over a crowd.
You can beat the game with zero in INT, AWA, and PERS. You'll miss a few dialogue options, and miss a few quests, but it's technically doable. Several advance skills require investment into INT, AWA or PERS, so keep that in mind, too.
Even if you wanted to invest heavily into physical traits such as STR, END and AGL, you are well served in tossing some points into the mental skills.
I -might- suggest raising INT, AWA and PER to Level 2 as a first go.