Are the prayers (Dhuhr, Asr) that the questioner performed while in a state of ritual impurity (junub) due to the unavailability of water valid, and is he accountable for his delay in asking about the ruling on this matter?

The prayers you performed with ablution while in a state of major ritual impurity (janabah) are invalid, and you must repeat them. A person in a state of janabah, if they cannot find water, should perform tayammum (dry ablution) and not wudu (wet ablution). Moreover, it is inconceivable that there would be no water in Riyadh, and its unavailability in your brother's apartment does not justify tayammum. Rather, you should have searched for nearby water or performed ghusl (ritual bath) with the mosque's water. Your obligation was to ask at that time, not after a month.