Actually changing a word from definite to indefinite by adding ال doesn't change the short vowel mark (al-ḥarakah الحركة) on the last letter. Only one thing might change: If the word ends with tanwin تنوين (nunation -un, -in, -an) (the addition of a final nūn sound to a noun or adjective to indicate that it is fully declinable and syntactically unmarked for definiteness), then tanwin changes to the convenient ḥarakah when adding ال: -un ٌ becomes ḍammah ضمة (a short /u/) -in ٍ becomes kasrah كسرة (a short /i/) -an ً becomes fatḥah فتحة (a short /a/) But no need to worry about that, because in colloquial Arabic we don't pronounce al-ḥarakah on the last letter. So we pronounce all words as if al-ḥarakah above the last letter is sukūn سكون (this ḥarakah indicates that the consonant to which it is attached is not followed by a vowel).

No. It depends on the function of the word. For example, If the singular word is subject, then it has damma on last letter. But if a singular word is the object, then it has fatha on the last letter. There are many other cases, I just wanted to give you examples. Hope this helps.