How can one avoid having ill thoughts of Allah and continue to supplicate, despite feeling that their prayers are not being answered and that they will not achieve their wishes in life?

I advise you to continue supplicating and persevering with good faith in Allah. Remember that hastening the response is one of the impediments to the acceptance of supplication, and it is not a condition that one receives exactly what they asked for. As in the Hadith: "The supplication of anyone of you is granted as long as he does not show impatience by saying, 'I supplicated but my supplication was not granted.'" And in another Hadith: "There is no Muslim on earth who supplicates to Allah with a supplication except that Allah grants it to him, or averts from him an equivalent amount of evil, as long as he does not supplicate for a sin or the cutting off of kinship ties."