How to calculate resolution of DFT with Hamming/Hann window?
The frequency resolution of a DFT is indeed significantly affected by the choice of window. Two key parameters to consider when selecting a window are the frequency resolution and dynamic range. The frequency resolution is the ability to discern two closely spaced frequencies at similar power levels (therefore a metric of what that spacing is would be the frequency resolution), while dynamic range is the ability to discern two signals at different frequencies and significantly different power levels; specifically the ability to see a low level signal in the presence of a much stronger signal (therefore a metric of what this power difference is would be the dynamic range). Typically a higher dynamic range is achieved by using appropriate windowing at the expense of frequency resolution. The highest frequency resolution that can be achieved is with a rectangular window (and the lowest loss; any other window will also introduce a processing loss). 

The Equivalent Noise Bandwidth (ENBW) is a commonly used metric for frequency resolution. The ENBW is the bandwidth (often given in FFT bins) of a brickwall filter that would result in the same noise power as the DFT "filter" for white noise (the DFT can be described as a bank of filters). For the rectangular window, the ENBW is one bin, but the poorest dynamic range (sidelobes with peaks rolling off at a $1/f$ rate in magnitude.  Any other windowing used would have a higher ENBW. 

For a given length N window function $w[n]$, the ENBW in bins is computed as follows:

$$ENBW = N \frac{\sum \left(w[n]\right)^2 }{\left(\sum w[n] \right)^2}$$

See this classic paper by fred harris tabulating the ENBW as well as other paramters of many commonly used windows. fred harris windowing

Below is a slide I have further depicting the ENBW for a rectangular window:



Below compares a N = 30 rectangular window (denoted the Dirichlet kernel) to a Blackman window of the same length. The decrease in level shown of -7.83 dB is the coherent gain for this particular window used. The coherent gain is simply the average of the window weights. The result below is is consistent with the coherent gain of 0.42 as listed for the Blackman window tabulated in the fred harris reference given; $20Log_{10}(0.42) = -7.54$ dB.  What is very clear from this picture is the significant increase in both dynamic range and frequency resolution.



The reason for not being an exact match to the tabulated results is the window length. As the window length approaches infinity the physical result approaches the tabulated, as shown in the figure below for coherent gain. For this reason caution must be applied when using the tabulated results for any smaller length windows.