Are the persistent thoughts and questions about God's power and will, such as "If God is powerful, why doesn't your heart stop beating?", which cause fear and confusion, considered a whisper (waswas) or disbelief (kufr), and is there any reason to fear a heart stoppage or God's punishment?

These are whispers from Satan, and their cure is to ignore them and not pay attention to them. Seek refuge in Allah from theing rejected Satan when they occur, and say: "I believe in Allah and His messengers." Occupy yourself with what benefits. These whispers do not harm faith as long as they are disliked and repulsive, and one is rewarded for striving against them. One must have a good opinion of Allah, strengthen trust in Him, and rely on Him. One may also consult trustworthy psychiatrists.