Regarding Jimmy...

[Berf]

Sorry, I didn't chime in at the right time.
But I can assure you that Patriot (or any other Robot) is not removed from play if it's healed between the use of Jimmy's Energetic boost and the and of the turn
As a matter of fact, it works that way with other abilities too, take for example the Pain-man, who can heal himself with the Medicinal herb TC in order to stay alive (if you play it right, that trick is priceless ). Or an ISC drone like the Samurai or the Serial Shenron can heal themselves while under the Grey Kitsune's Binary possession ability.
In short ,as long as your fighter is not incapacitated when the ability preventing him from being removed from play stops being effective, he stays on the field