1. Is it allowed to combine Zuhr and Asr or Maghrib and Isha why one is traveling?
2. If the first Sajda (prostration) on the Fajr Salah was performed within the time of Fajr but the time of Fajr had already finished when Salah was completed, is this Salah Valid?
1. Generally, combining two Salah in one period of Salah (e.g. performing Zuhr Salah during the time of Asr, or performing Asr Salah in the time of Zuhr) is not permissible while in travel nor is it permissible at home. If one does this the only one Salah (i.e. the Salah for that time) will be valid and he will still be responsible for performing the other Salah. However, there is nothing wrong if while travelling, one combines two Salah for ease and convenience in such a way that he delays a Salah (e.g. Zuhr) until the end of its time and performs the next Salah (e.g. Asr) in the beginning of its time.
2. If the Fajr Salah was not completed before the rising of the sun, then it is invalid and one must repeat is afterwards. Furthermore, with regards to the Hadith that is attached to the question, the Muhaditheen has given many different explanations to it. Alama Tahawi has mentioned that the law mentioned in this hadith is for that person who Salah is compulsory upon him for the first time, like a child who just entered the age of maturity, one who just became a new muslim, a woman who just came out of her menstruation period etc. If any one of them, during the time of Fajr or Asr, has only that amount of time in which they can perform only one Rakat, then it is mandatory upon then to perform the entire Salah and Qaza will also be incumbent afterwards. This is why the law in this Hadith is not for general cases.
And Allah knows best.