Most of the research into this is Japanese, but the results are remarkably consistent across all of Japan with a wide range of body sizes and climates and the results also match what I've observed.
The gestation period of sika based on captive deer was determined to be 231 days. Research on wild sika gave a gestation period of 231.6 days.
It is found that large variations in the date of conception may be seen but that there tends to be a very marked peak and it is interesting to note that the peak in the Japanese studies (22nd October in the particular one I'm looking at for this info) would also be reasonable for the UK. Several Japanese studies found the range of dates of conception to be as follows:
7 Oct - 17 Jan
8 Sept - 11 Dec
9 Sept - 23 Jan
12 Sept - 22 Dec
The date on which calves are born, and these are based on different studies to the ones above and so will have had slightly different distributions of conception dates, was found to peak in late May/early June but in some studies calves were born as early as April and as late as November.
Interestingly the view in the Japanese research is that the rut "occurs immediately after the peak of fat deposit of male sika deer." So while we always look to the current weather conditions to provide info on the progress of the rut it may be that it is actually driven by the conditions required to lay down fat in stags and, in turn, this may depend on the weather or other conditions across the whole summer period.
In terms of twins one researcher had seen only two cases of twins in 15 years while another reports the twinning rate to be 0.29%. In a deer farm in China the twinning rate was reported to be 10.4% and this was attributed to long term selective breeding to improve the farm stock rather than to nutrition or other factors.
Hopefully someone finds that interesting. I'm just reading this stuff in a book and make no claims to being an expert so the best I can say is that this fits with my experiences.