Is the statement of a male relative who has not proposed that he does not outwardly perceive an inclination towards the questioner considered a sign of a turning away after performing Istikhara? And is it permissible to supplicate that Allah put love for the questioner in his heart after performing Istikhara?

It is permissible to supplicate that Allah incline the heart of a person of religion and good character towards you for the purpose of marriage, and there is no harm in that. Istikhara (seeking guidance from Allah) is performed for permissible matters where one is unaware of the better course, and not for the persistence of love for a specific person. Therefore, it is incorrect to speak of an istikhara sign in this context. What is legislated in such cases is general supplication. Love before marriage is forbidden in Islamic law, except for that which occurs unintentionally and one restrains oneself from the forbidden. If marriage becomes easy, then praise be to Allah. If it does not, do not tie your destiny to it. Entrust your affair to Allah and ask Him for a righteous spouse, for Allah knows what is good: "And perhaps you dislike a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not" (Al-Baqarah: 216).