I am not aware of any examples of the caculation you are seeking but offer the below answers to your basic questions.
1. Yes, actually the heat transfer will be both ways in the region of your tank your tank will be heated and it surrounding air will be cooled. If your tank were to be confined to a very small confined and insulated region then this process would continue until both the tank and the surrounding air achieved the same temperature. Under open region conditions, the (downward) convection of the tank's surrounding air will raise the temperature of the tank to the ambient temperature of general surrounding region.
2. First, an example of the difference between "surrounding" and "ambient" temperature is that the air in the immeadiate region surrounding your tank will be lowered by contact with the cooler tank wall and therefore cooler than the "ambient" temperature of the general region surrounding the tank. Second, when exposed to the sun, the tank will experience radient heating independent of the convective air heating.
3. Convection can be either upward or downward although the term is not generally thought of in that manner. Adiabatic winds in mountainous regions whereby air is cooled by snow at the high regions of the mountains flows down the mountian sides are an example.
4. If there is any significant forced (wind) flow around the tank then it will increase the heat transfer rate.
In all cases the rate of transfer is going to be a combined effect of tank vs. air temperature differential, combined air flow and radiant heating effects: plus, in a large tank, the convective and conductive heat flow of the tank liquid. The tank shape and orientation are also factors. In other words, you are dealing with a very complex combination of factors that to get a truly accurate solution requires a computer heat flow program analysis.