Is it permissible to say "Ya Marhaba" or "Ya Hala"? Is there any polytheism (shirk) in uttering them in this form? And is it permissible to say "Badahaha" or "Badihi waqa'a hadha al-amr" (This matter occurred by intuition/obviousness)?

A person is permitted to say to their guest or caller: "Ya marhaban" (Welcome) or "Ya ahlan" (Welcome), because the intent of this address is merely to greet. As for polytheistic calls (nida' shirkī), they are those intended for seeking aid from one who cannot respond except Allah, such as saying: "Ya Jilani, relieve my distress." Similarly, there is no harm in saying "It occurred spontaneously" or "It is natural for this to happen," as long as one does not intend that the matter came into existence without a Creator. The criterion in these matters lies in the speaker's intention.