I've had some problems with the aspirations, too.
For Soulmate Aspiration and apologizing, I tried it a couple of things (saving before testing different methods), and what finally worked for me was this: I had both spouses angry. Then I had the one who needed to apologize insult the other. At that point, the option to beg forgiveness came up. After doing that, the smooth apology option was available, and that met the requirement. On one of my earlier tries, doing the smooth apology alone hadn't worked, and neither had only having one angry spouse.
For the BFF issue, with either the Soulmate aspiration or with the Friend to the World, I could only get one BFF at a time. I'm fairly sure it's not a matter of the correct interactions, as I was able to ask to be best friends on the first interaction with a my new bff after destroying the relationship with the old bff. For your own BFF count, you can use mean interactions or a cheat to lower the relationship quite a ways, and they will stop being BFF, letting you ask someone else. It is then possible to rebuild the relationship, and begging forgiveness helps a bit with that. I found the relationships improve fastest in one-on-one conversations, so I invited my sim's friends to my lot one at a time to become BFF and then destroy and fix the relationship.
For the Soulmate aspiration, if it's your sim with the BFF the above should work. If it's the fiance who already has a bff, you could either switch to play him or her, or you could move them in. Once you control them, you can trash their BFF and work on the couple's relationship. I'm not sure if you have to be bff before marriage or not - can they become BFF after marriage? I had my sims reach BFF before starting a romantic relationship so didn't test this.
If you are not adverse to cheats, the list on the sims forum has one for relationships. After having gone through 4 relationship trash-and-rebuilds with Friend to the World, I got fed up and cheated to fix the BFF mess before romancing the intended spouse.
http://forums.thesims.com/en_US/discussion/778600/ive-compiled-an-extended-list-of-cheats-and-commands/p1modifyrelationship YourSimFirst YourSimLast TargetSimFirst TargetSimLast (-)50 Track_type
where Track_type is either Friendship_Main or Romance_Main, and the number is the amount to raise or lower the relationship bar. I used -80 for lowering the relationship. I got a notification they were no longer BFF, then I used the cheat again but with 80 and the bar refilled to where it had been and they were now good friends. That left the friendship intact, and my sim then became bff with the intended spouse.
At first, with the Friend to the World aspiration, I thought that allowing only one BFF could be deliberate, to make the aspiration more challenging. However, as the soulmate aspiration also requires a BFF and the fiance is likely not under player control until the wedding but might already have a bff, I now think it's a coding mistake.