All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
What a traveler is permitted to do when travelling, like shortening and combining the prayers, can only be done after he actually starts his journey and leaves the town where he lives; for more benefit, please refer to Fatwa 83821.
Therefore, if you are travelling before the ‘Asr prayer and you predominantly think that you will arrive after the expiry of the time of the ‘Asr prayer, then you are obliged to perform the ‘Asr prayer during your travel after the time of ‘Asr starts. You should either get off (from your means of transportation) at a place where you may perform the prayer if possible, or you should pray while on your means of transport. If you need to perform ablution and you are unable to do so, then you may perform Tayammum (dry ablution), and if again you are unable to perform Tayammum, then you may perform the prayer as you are in your condition and you should not wait until the time of the prayer ends. For more benefit, refer to Fatwa 86380.
As regards your question about the missed prayers during travel, then we have already clarified to you that you are not permitted to abandon the prayer during travel or not perform it until its time ends; you should either combine the two prayers at the time of the first prayer or at the time of the second prayer, or that you pray during your travel according to your situation.
With regard to making up for the missed prayers, then it is an obligation to make them up as soon as you become able to do so, because the Prophet said: “Whoever forgets a prayer, he has to perform it as soon as he remembers it because its expiation is to pray it as soon as he remembers it.” [Bukhari and Muslim]
For more benefit, please refer to Fatwa 89978.
Allaah Knows best.