For the shapeshifter, the +2 modifier applies only to CHA.
So if you rolled a 10 and attributed them 5 EP in CHA then they have 7. Their STR stays at 5 because there is no modifier for STR.
So they have CHA 7 and STR 5. Their HP would be 7 (half of your roll, plus the HP modifier which is +2: 5+2=7).
And yes, they would need to spend 3 EP from STR for a total success at busting down a door, because STR is the relevant Stat.