Changing plug switch to fan and making plug constant hot
The issue with tapping in like that is slack
In order to have a legally (and practically) wire-able junction box, you need to have a sufficient length of cable coming in (about 6&quot;) so that connections can be made without having to reach all the way into the back of the box.  The problem is, your average wiring run doesn't have 8&quot; of slack length in it to deal with having a 4&quot; fan-rated round or octagon box cut into the middle of the run.  Solving this problem requires either an additional box or a special NM splice kit to splice an additional length of NM cable into the circuit so that sufficient wire length's available in the box where you're making your connections.
Once you have that solved...
Once you have the fan-rated box up and the wire length issues worked out, we can then focus on re-wiring.  The red wire in the switch-box-to-B cable gets abandoned  and capped off by itself at all ends (although if you're using a NM splice kit, it can't terminate there!), and all the grounds get connected together and to the box in the new fan box, of course.  Once that's done, the fan box wiring is as per the instructions, just with an additional black and white in there to pass power on to the receptacle.  Finally, switch B and the always-hot pigtail feeding it can be removed (if you want, you can get a battery-operated wall controller from Kichler that works with the remote for your fan, part #370039MULTR, and install it in place of switch B although you may have to swap the wallplate at that location to a toggle+decorator type to do so), and the receptacle at B can be replaced with one whose tab has not been broken off.