In the Aruch HaShulchan OH 581:4, he writes regarding the selichos we recite before Rosh HaShanah:
האחת: דאלו שאינם מתענים, ובהסליחה מוזכר לשון "תענית" או "צום" – לא יאמרו זה, דלא ליהוי כדובר שקרים. ויאמרו לשון תפלה במקום תענית
That if the selicha mentions fasting and the person reciting it is not fasting, then he should not mention the fast, but should change the word to "prayer" instead of "fast", in order that he should not be speaking falsely.
1) Is this rule against speaking falsely in prayer a general rule? Source?
2) If so, does it refer only to factual matters (like whether one is fasting, or in the case of nachem, whether Jerusalem is in point of fact in ruin), or does it refer also to theological matters? Meaning if one doesn't believe the text of a particular prayer, should he alter it accordingly?