Those fans have their own fuse up in the fan area you might have blown. (one version has a pop-out glass fuse)
One version has a rocker switch for fan direction. If that is in the middle with no direction selected the fan will not run.
You only need a converter, forget the regulator idea. If it is not too late you might want to return that one for their two-stage version. The original one-stage like you got was a mistake, where they thought an LFP could float on 14.x for an extended time, or else they expected you to not float the LFP at all.
Your plan to disconnect the battery when on shore power should be ok though. Just remember to do that if you will be on shore power for a long time. If you got the two-stage it would drop to 13.6 and float the LFP safely so you would not need to disconnect it.