I went in November and didn't use any mosquito repellent. It may depend on what time of year you're going.

I'm afraid that days trips are prohibited. In order to even enter Havasupai territory, an overnight reservation (which includes the required permit) is needed -- and a stay of two nights is really a practical minimum. As you stated, the Lodge is completely booked for all of 2019. Reservations for the campground for 2019 open up on 1 February 2019, at 8 am Arizona time. They sell out almost instantly. If you are interested in the campground, go to tripadvisor's "Supai, Arizona" forum for details. If you manage to get a reservation, helicopter flights are sometimes available from the trailhead (Havasupai Hilltop). They don't fly every day, and there are other qualifications. In addition, the process of getting a ride is changing this year. As above, tripadvisor's Supai forum is the best place to discuss this.

I assume you already have the required reservation/permit, which must be obtained in advance. Everything is sold out for 2018. When you say you are time limited, do you mean you only have a one night reservation? Day hikes are prohibited. A riding horse is $250 one way. If you have anything more than a 10 pound day pack, you'll also have to rent a pack mule ($132 one way, but it can carry bags for more than one person). With limited time, the quickest way to get to Supai is to hike. Drive to the trailhead the evening before, and start hiking at or before dawn. Horses don't begin the trip until hours later, and will arrive at Supai later than early hikers. There's also a helicopter, but it only operates four days a week, doesn't take reservations, may have a huge line, and doesn't start until later in the morning.

A tour guide is not needed. This is a safe hike with respect to dangers from humans and animals. Since 1965, there have been no recorded tourist deaths from animal attacks, and only one murder in that 50 year period. There are occasional deaths, mostly from foolish choices (e.g., cliff diving, hiking during a flash flood, swimming under a waterfall, possibly a couple of heat-related deaths), but overall it's pretty safe. If you're experienced hikers, it should be no problem. The Lodge is like any modest motel, so you don't need to bring bedding or towels. There's a small store in town, as well as a cafe, so you only need to bring enough food and water for the hike (plus perhaps a small emergency stash). Note that The Lodge is sold out for pretty much all of 2018 - unlike the campground, reservations open up in June for all of the following year. There's a lot more information at the official Havasupai website, or you can ask more questions at the tripadvisor forum for Supai, Arizona.

You do not have to go with a tour or guide. But you do have to have a reservation at the campground or the lodge. Your reservation process will include all permits. The only way to reserve a camp spot or a room at the lodge is by contacting them by phone. There are no reservations on the web. Contact phone numbers are on their website. It can be difficult to reach them - the phone often rings with no answer. I tried for 6 months before I reached them. If you prefer to go with a guide a know a reputable company Wildland Trekking has trips.

Water stays about 70 degrees all year long - which is not that warm. Feels great when it is 100 degrees out but not when it is 70 degrees out. Winter months are chilly but very manageable if you plan for it (much better than scorching 110 degree summer heat if you ask me). Lodge is about $140 per night with some associated entrance fees. You can likely use weather website to see average monthly temps. Search both for Peach Springs temps and Supai (Supai Village) temps. The website they have is pretty good but not an abundance of info. It can be very difficult to get connected via phone - I called for 6 months before I got through (no reservations made via web - phone only). I recommend reading Exploring Havasupai by Greg Witt. And it is worth noting - this is not Grand Canyon proper, Havasupai is 190 miles away from Grand Canyon South Rim entrance.

Yes we had permits. We stayed in Peach Springs about 60 miles from Trailhead.

Since you asked about hotels, it seems that you do not yet have the required reservation and permit, without which you are not allowed to even enter Havasupai territory. Permits are pretty much sold out until at least November. Day hikes are not allowed. Visiting Supai requires planning far in advance. In order to get a room at the only lodge, you'll need to call twelve months or more in advance. The only other option -- a campground -- opens its reservation line on February 1 for the entire year; it is fiendishly difficult to get through before all dates are sold out. Without a reservation at either the lodge or the campground, you are not allowed to enter Havasupai territory.