Shortening the prayers is a confirmed Sunnah for all travellers, whereas joining the prayers is permissible but is not Sunnah, but it may be Sunnah and recommended if there is some difficulty involved in not doing it.

After relieving oneself, it is obligatory to remove impurity, whether it is removed with water or something else, such as stones or paper or tissues, but using water is best.

If you touch a dog when it is not wet, then your hand does not become impure. If you touch a dog when it is wet, this means that the hand becomes impure and must be washed seven times, one of which should be with earth.

The reason why it is recommended to seek refuge with Allah when entering the toilet is to seek protection with Him from the devils that frequent places where there are impurities and where ‘awrahs are uncovered.