Physical Exercise as a Monk? Is a monk allowed to exercise the body in order to keep it fit and healthy? I reckon both 'healthy' and 'fit' as attachments, but is there an overall rule/teaching that explains this?
Healthy and fit body does not need to be seen as an attachment. If a monk took the Bodhisattva Vow, all his activities will be done with the wish to benefit others. A healthy body is actually a very useful tool if one wants to help other beings. During a long life free from illnesses one can do much more than during a short life with numerous visits to doctors and hospitals (which are usually costly). Precious human body is also a topic of various teachings (see this or that) which invite us to realise how rare it is to obtain a well-functioning human body and how easy it is to lose it. With that in mind, maintaining a healthy body is a very wise thing to do.

In Tibetan Buddhism one of the main meditation practices involves doing physical  prostrations. In Vajrayana traditions all practitioners - monks and lay ones - need to complete at least 100.000 prostrations as a part of preliminary practices. Some practitioners continue to do prostrations on daily basis and even Dalai Lama admitted that he indeed does them every day.