Of Hindi and the verbs

I have never been a good student of any language, as is evident from my posts. I am a tamilian by birth, but can carry a conversation, thats it. I am brought up in Delhi and had so many Punjabi friends but never ever tried to learn Punjabi. Now in Mumbai, and I am still struggling with Marathi. I have scored decent marks in English, Hindi and Sanskrit (my third optional language), but never have I seen those brilliant numbers. I have been more inclined towards maths and sciences.

Recently, while going over Hindi with my daughter, I was back to that nagging question for which I never tried to find any answer and never got any.
I tried to compare the 4 languages I know (including sanskrit).
I have observed that in English, we do not associate gender to the verb. So, he is coming, she is coming, bus is coming, rain is coming. Thank God for that!
In Tamil and Sanskrit, we have genders with verbs, but then there are 3 genders - masculine, feminine and neutral. So, "avan varan" (he is coming), "aval varaal" (she is coming), "bus varudu" (bus is coming). In case of inanimate objects, we have the third option.
I get stuck when it comes to Hindi. There is gender in verbs but there is no third gender. Is Bus masculine or feminine? What about Chair? "Bus aa raha hai" or "Bus aa rahi hai" (Bus is coming)? If "Baarish ho rahi hai" (its raining but with feminine verb) then why is it "Paani baras raha hai" (again its raining but with the usage of the word water and masculine verb). “Mobile baja” or “mobile baji” (Mobile rang)?
Reminds me of the hilarious issue raked up in the movie Chupke Chupke… on the difference in pronunciation of “cut”, “but” and “put” even though they all are spelt the same way!

Any Hindi teacher around? How do I correct my kids when I don’t have my basics right?