Is it permissible to prostrate on the bed for the prostration of recitation (sajdat al-tilawah), and is it obligatory to face the Qibla?

It is permissible to prostrate on a bed if it is connected to the ground. For a prostration of recitation (sajdat al-tilawah), the conditions of prayer must be met: purity from ritual impurity (hadath) and filth (khabath), covering of the 'awrah, and facing the Qiblah. Therefore, it is not valid to prostrate in any direction other than the Qiblah.