You can do thirumanjanam for the Padhuka after sankalpam and offer fruits, it is not a must that you should do this every day. It can be done on special occasions.
It is considered special when one does Padhuka aradhanam every day as per the tradition of Srimad Andavan.
It is not stipulated that Padhukas had to be carried during travel. If a thirunakshatram of Acarya coincides with travel, then Padhukas can be carried along. It should be carried with utmost reverence like how Perumal is carried. Maintaining purity is important while carrying Padhukas.