What are the possible conditions at Mount Aragats in October? Does it require climbing equipment to climb the highest pick? What are the possibilities to get there from/to Tbilisi and from/to Yerevan? Is it possible to climb without a guide?
Obviously some aspects of weather can't be predicted, and will vary from day to day. However, you can give yourself a guide and estimate by considering general conditions, and other climbers' past experiences.
For a past experience in October, I recommend having a look at this blog: The first of October aka. the day I finally climbed the north summit of Mt. Aragats… . He may even be worth contacting for more details.
Then looking at the current forecast and climate for the mountain shows this week (conveniently, October) to be light snow and snow showers.
Armeniapedia actually has a writeup of the various routes, and from there it sounds like you can mostly walk it, although they do recommend boots and layers.
Lonely Planet points out that the southern peak is easy enough for even inexperienced climbers, but the northernmost one requires crossing a snowfield, and will require experience. They also recommend a company and guide, if you wish to use one.
Climbing Mount Arragats in October is totally fine. I did it by myself. Just you have to be sure about timing as the days are shorter. Also it is much colder.
You don't need a guide, but you have to be well prepared and know what are you doing. Especially on the North summit, the last ridge is pretty dangerous!
There is no mandatory guide needed and there are no entrance fees or permit fees for climbing this mountain.