Travel Advice

Hello, I have tentatively planned a trip to Jaipur and was looking into squeezing in Agra as well, mainly to see the Taj Mahal. I have visited it before, but this time I’m traveling with family (wife, parents, kids). I wanted to get this community’s thoughts on my plan: fly in to Agra in the afternoon on the 13th of January. Stay the night and leave next day to Jaipur via Ajmer express at 14.40 from Agra fort station. A few questions: 1. Is there sufficient time to visit the Taj in a relaxed manner in the morning of the 14th, then return to the hotel, check out and have lunch in time to catch the train at 14.40 from Agra fort station? 2. What would you recommend we do in the evening of the 13th? 3. Are flights and trains reliable at this time of the year? Any risk of fog/smog that can mess up the plans? 4. Any risk of fog affecting the view of the Taj altogether? That is, even if there is smog early in the morning, would it generally clear up by mid morning? Or could we end up not seeing the Taj properly at all? 5. Also, any hotel recommendations? Close enough to the Taj and the railways station and is also an upscale (but not too luxurious) and family friendly?