All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
1) Performing the funeral prayer without ablution is not permissible, since purification is a prerequisite for the prayer. In other words, the prayer is null and void without purification. So, it is a blunder to say that prayer is permissible without ablution.
Moreover, although there is no Rukoo' nor Sujud in the funeral prayer, it is still a form of prayer that necessitates the requirements of prayer in general.
2) According to the dominant opinion among scholars of Islam, one is recommended to shorten prayer on a journey; i.e., it is not mandatory. So, it is better to shorten the prayers on a journey although one is permitted to perform one's prayers in their normal state.
However, if a traveler performs his prayer with a resident Imam; i.e., in congregation, then it becomes obligatory on him to perform the prayer in its complete and full state.
Allah knows best.