How do we determine molecule chirality in these examples?
Although you have arrived at the correct answers and seem to have followed a reasonable process for getting there, it's important to be precise with the use of terms like symmetry and chirality. For a molecule to be chiral, it must be non-superposable with its mirror image. It's important to really embed this definition before talking about symmetry and things like chiral centres. For example, it is possible for molecules to be chiral without any chiral centres, and it's possible for molecules with multiple chiral centres to be achiral.


the guaranteed way to determine if a molecule is chiral: draw (or build a model) of the mirror image and determine whether they are superposable


Now, symmetry is a different, but related, topic. A molecule with a point or plane of symmetry will be achiral. However, molecules with a rotational axis of symmetry can still be chiral, eg. many often-used chiral ligands are C2 symmetric.

So, in answer to your question, "What am I missing? - I would just say: the rigor in use of the terminology. Your approach of drawing different conformers of the molecules with two chiral centres and looking for a plane of symmetry (that shows the molecule is a meso compound, and therefore achiral) is sound and led you to the correct answers.