Is it permissible to perform ghusl if one is unable to complete it, while having doubts about the water covering all parts of the body and penetrating the hair, and wishing to pray at the current time with the possibility of repeating it later?

Overwhelming probability is sufficient for covering the entire body with water during ghusl (ritual bath). If you are overwhelmingly certain that water has reached your entire body and the roots of your hair, then your ghusl is valid. However, in case of doubt, the default is that one's obligation has not been fulfilled. Therefore, you must wash the areas you doubt water has reached. There is no need to repeat the entire ghusl, as continuity (muwalat) is not a condition for its validity according to the majority of scholars. However, you must renew your intention for washing the rest of your body.