Palestine is a “first-to-file” jurisdiction, which means that trademark rights are obtained through registration, not through use. Only in some exceptional cases can an unregistered trademark be protected, so registration is essential to secure exclusive rights and to act against infringements.
It is not necessary for the trademark to be in use in Palestine in order to file and obtain registration.
If you register a combined trademark (with both word and figurative/logo elements), the exclusive right is limited to the exact configuration in which it was filed and registered. If you want to use and protect the word element separately from the logo (or vice versa), it is advisable to file separate applications for the elements you wish to protect individually.