1) Is Dumbledore alive?
No. He is not. He was killed during a skirmish at the ministry. A new headmaster was appointed to be in charge of Hogwarts.
2) Who is the minister?
Great Britain is lacking an 'organized' minister of magic at the moment. The Death Eaters have taken over the original location of the ministry of magic, but the Order has their own power as well, having quite a large support group of their own. If it had to be said who has the most power at the moment, it would be Rodolphus Lestrange, who is basically pulling the strings of the Death Eaters. Vincinte Catchlove is not too far behind him for the Order's side, however. Everything in wizarding UK is just extremely unorganized for the time being and everyone is walking on eggshells.
3) How did Voldemort die?
Because Voldemort had not created any Horcruxes, he didn't have any supernatural pillow to keep him from dying when his curse reverberated off of little Harry Potter and hit his silly face. So off he went to Hades.
4) What's going on at Hogwarts?
Basically, since everything went topsy-turvy after Dumbledore was killed and a new headmaster was elected, there were many changes in staffing; either by choice or because some of the teachers were killed during the heavy fighting. We're not sticking with who may or may not have been teaching during the canon time-line because of this. Other than this, things are pretty much going the same as would be expected, just differences in staffing and such. This makes it easier for you to make a professor if you want :D
4) Can I make a muggle death eater, order member, etc? Basically a muggle that is fully involved in the war?
No. Why? Just no. One. because it makes no sense, especially to have a muggle DEATH EATER. Think before ya speak, child! And two...? I dunno. There is a lot of reasons. I will not list them all out. Mainly, because we do not allow Mary/Gary Stues here, so unless you have CONSIDERABLE REASONING behind your muggle/squib being part of anything, they will not be.
5) Can I play a student as well as an adult?
Yes, although we would love if you would get your first character involved in at least one or two threads before you start with another.