The questions that you are asking are too general. You should first spend a bunch of time at the State of Alaska site. It will answer many of your general questions and list the current regs plus provide moose density info, etc.Costs of licenses & tags are there too. That site is at:
www.wildlife.alaska.gov Then you can get specfic with your ??
But a quick answer to the seasons is from the last cuple of weeks in aug to the end of sept depending on where you plan to go. The rut generally kicks off about the second week of sept. Read the regs carefully no only as to seasons but as to tags available to non-residents. We have several types of tags including draw, otc,cultural, etc
As far as the weather that you can expect well that can be anywhere fronm the 60's down to the below zeros. Plus snow or rain or wind or all of the above. Go to the Noaa site for Alaska and you can see the weather history for the areas that you are plnning to hunt.
Also hit the mil site or naval observatory sites for sunrise sun set info as at that time of year we are loosing up to 7 minutes a day depending on area.
Then come back and ask some more questions to help narrow down areas (units). transport, gear, etc.