Is divine inspiration after Salatul Istikhara limited to nocturnal dreams, or can it come while awake? And is it true to believe that divine inspiration occurs only for strong believers?

It is not necessary to see a vision after performing Istikhara; rather, one relies on the feeling of ease or unease in the heart. If the heart feels at ease, one proceeds with the matter; if not, one abandons it. This feeling of ease occurs while awake and does not require strong faith, because Allah answers the supplication of the one who supplicates. The hadith of Jabir explains the method of Istikhara prayer and its supplication.