I heard that RasoolAllah SAWW used to exercise. Is that true, and if so then how exactly?
I also heard that he kept a flat stomach, is this true also?
What was his diet like and how often did he eat meat?

Yes our Rasul saw had balanced diet
He used to work hard and he never asked anybody to assist him but he always assist others. Best exercise engage yourself in work and organise your time of work and Rest .
He used to had two meals in a day.
As quran instructed
يَا بَنِي آدَمَ خُذُوا زِينَتَكُمْ عِندَ كُلِّ مَسْجِدٍ وَكُلُوا وَاشْرَبُوا وَلَا تُسْرِفُوا إِنَّهُ لَا يُحِبُّ الْمُسْرِفِينَ

O children of Adam! attend to your embellishments at every time of prayer, and eat and drink and be not extravagant; surely He does not love the extravagant.
His diet was milk, Date, Olive, barely bread and mutton on occasion