Sometimes my party warns me about a secret wall I`m passing, sometimes they don`t.

What determines, if they do that?
Is it any ability, that is necessary for that?

What do I have to get always such a hint?

Good question.
If my memory serves me correctly, dwarves are good at finding secret doors, while elves are good at finding illusions.
But I have no idea if this game uses this mechanic. Can't find it in the manual and cluebook either.

I'm going to guess that it's purely based on your current level.

Perhaps someone else has a better answer.

No idea, I had elf mage, half-elf cleric, human paladin and dwarf fighter/thief. And sometimes companion NPCs spotted the odd wall, sometimes different characters among my party did this. Some illusions were spotted only with my mage though. I think all such cases are story driven and impossible to miss. Some illusion walls however never caught attention of my party yet they held quest related items. Cleric Level 5 spell - True Seeing
Mage Level 6 spell - True Seeing
* - you will not get a hint, but see through illusionary walls, I don't think you'll get more hints than your team can handle, it's advised to get different races and classes to get as much as possible, but I don't think elf mage would see more than human mage, however no mage in party will definitely leave you without some hints.

Good luck in case you created multiclass mage or cleric.

Usually my dwarven fighter/thief spots those hidden entrances and buttons. I think a dwarf gets a bonus and being a thief might help as well.

There are some analysis tools available with the All Seeing Eye tools which can help track this down.

From memory, most of the "secret door" hints are triggered through a combination of factors:
1) A "level flag" (to prevent the hint from appearing twice, the flag is set after it is shown)
2) Various classes or races (different ones will trigger different advice)
3) Random chance - there is a chance that you won't receive the hint the first time you pass by, but you can trigger it by passing by the square again