(1) In English, we have an expression "pull the wool over one's eyes," which means to "deceive someone." Here, the author wrote "the white tulle" instead of "wool" because she was talking about her wedding, so she was being figurative, by replacing "wool" with "white tulle." (Note: A white tulle is a wedding veil). (2) No, "walk down the aisle" could have a literal meaning as well: E.g., "I walked down the aisle on the crowded airplane to get to the restrooms." (3) Yes, "in my heart of hearts" is an expression that emphasizes "in my heart," that is, the woman wants to be absolutely certain that her marriage will last forever.

When she says she'd rather "pull the white tulle over my eyes" as in she's pulling it over her own eyes, it means she'd rather ignore the possibility than to admit the possibility exists, thereby deceiving herself.