(1) The dating of the site is discussed quite intelligibly here: https://www.dainst.blog/the-tepe-telegrams/2016/06/22/how-old-ist-it-dating-gobekli-tepe/ Based on radiocarbon dates and the stratigraphy of cultural layers (mostly lithic points), it can be confidently dated more-or-less from 10,000 BCE to 8000 BCE, corresponding with the end of Pre-Pottery Neolithic "A" to the middle of "B".

(2) The development of agriculture in Southwest Asia has been researched extensively, which is good because it means there's a ton of material, but also unfortunate because it makes it a large and complicated topic, difficult to summarize. The tricky part is really in deciding what constitutes the beginning of agriculture and when to differentiate domestication from prior food ecology practices.

The earliest evidence of cereal domestication in the region goes back to at least 13,000 years ago, further to the south at Abu Hureyra: http://hol.sagepub.com/content/11/4/383 "New evidence of Lateglacial cereal cultivation at Abu Hureyra on the Euphrates," Hillman et al 2001

This is tangential but interesting, bread actually predates cereal agriculture, as there's evidence of flatbread made from wild einkorn and club-rush tubers from 14,400 ya - https://www.pnas.org/content/115/31/7925 "Archaeobotanical evidence reveals the origins of bread 14,400 years ago in northeastern Jordan" Arranz-Otaegui et al 2018

Here are some overviews of the origins of agriculture in general: https://www.journals.uchicago.edu/doi/10.1086/659307 "The Origins of Agriculture in the Near East" Zeder, 2011

"A contextual approach to the emergence of Agriculture in SW Asia - Reconstructing Early neolithic Plant-Food production" Asouti and Fuller 2013 https://www.jstor.org/stable/10.1086/670679

• Notable for arguing for the dissociation of early plant domestication from sedentary villages, which is relevant to the third part of your question. The traditional view had conceptualized the development of agriculture as being intrinsically linked to sedentary settlements, whereas we now have ample evidence of non-sedentary forms of domestication and agriculture. Also see "From foraging to farming in the southern Levant: the development of Epipalaeolithic and Pre-pottery Neolithic plant management strategies" Asouti and Fuller 2011, DOI 10.1007/s00334-011-0332-0

and "From Intermediate Economies to Agriculture: Trends in wild food use, domestication and cultivation among early villages in Southwest Asia" Fuller et al 2018, https://www.jstor.org/stable/10.2307/26595375

(3) For Göbekli Tepe specifically, see this paper: https://www.researchgate.net/publication/260198406 "Gobekli Tepe: Agriculture and Domestication" Peters et al 2014

Under the section on "Subsistence" they point out that the size of the site clearly suggests large-scale food procurement, but that there's not much evidence of plant processing en masse, aside from lots of grinding stones:

Storage facilities have not been found so far and remains of edible plants are rare. Up to now, only wild taxa including cereals such as einkorn, wheat/rye, and barley could be identified (Neef 2003). At this stage of research, however, activities pointing at cereal cultivation can neither be evidenced nor excluded.

Emphasis added. So basically, early agricultural domestication of plants had begun at some regional sites by this period and was an ongoing process for several millennia before and after, but we don't know whether or not any deliberate cultivation was practiced here. It is clear that hunting was a big part of the diet, mostly of gazelle and wild cattle.

One thing worth noting is Harlan's famous 1967 wild wheat harvesting study: Harlan, J.R. 1967. "A wild wheat harvest in Turkey". Archaeology 20:197-201

and followup: Harlan, J. 1992. "Wild grass seed harvesting and implications for domestication"

which showed that large amounts of cereal grains could be harvested relatively quickly from wild stands in the area, such that even without intentional cultivation, large-scale social projects could have been enabled simply from the surplus of wild foods.

This article goes into considerable depth on the question of pre-agricultural proto-farming and the process of domestication: "Identifying pre-domestication cultivation using multivariate analysis" by S. Colledge http://www.bioversityinternational.org/fileadmin/bioversity/publications/Web_version/47/ch08.htm

So in brief, my answers to your questions would be:

1. The dating is solid, 2. some form of agriculture had already begun in the area but in a limited and conditional fashion, and 3. the architecture at Göbekli Tepe certainly predates what we might typically think of as "agriculture" in the form of large-scale urban agrarian states, but doesn't seem to predate the earliest forms of semi-sedentary or non-sedentary plant domestication practices.

It'd be worth comparing Göbekli Tepe to other nearby sites like Abu Hureyra, from ~9500 BC - 7000 BC, which had at least two major phases of settlement, the former as a non-agricultural village and the latter as an early example of settled agriculture - and Çatalhöyük, around 7000 BC, which was a large proto-city with intricate housing architecture.