If a Hungarian word ends in -a and you "close" it by adding an ending, then (with few exceptions), it lengthens to á. (The same is true for e changing to é.)

base form lámpa → accusative lámpát or plural lámpák

base form példa ("example") → példát, példák, etc.

But if the word ends in a consonant, and it acquires a new a as a linking vowel to prevent consonants running together, then that new linking vowel will be an unaccented a.

ház → házak, házat, ...

Only on the first Wednesday of every month. But I'm not sure what you mean.
On "házat" vs. "házát", no, the "a" does not change, at least not in this case. The second "á" in "házát" is actually a different suffix.

"Ház" - "ház-at" - house in accusative. The "a" is just a buffer sound, to ease pronunciation. It is never "á".

"Ház" - "ház-a-t" - that is his/her house, in accusative:

• ház - house
• háza - his/her house
• házát - his/her house in accusative. Here, the "a" changed to "á". Because it was part of a word that later got the "-t" suffix, to make it accusative.

Not if they're in front of a noun - they don't take case or number (plural) endings then.