timeline in question: 300BC - 300CE (Pagan Celtic Ireland)
Quite a few questions, so I’ll condense them into bullet points:
1-What did Irish culture and religious practices look like before Christianity entered the island?Where there any common sports, activities, or practices that perpetuated everyday life?
2-how did technology, agriculture, and architecture on the island compare to the Roman and or non-Irish Celtic world world? Was Ireland completely isolated in technological advancement? What technology did ancient Ireland have?
3-how did ancient Irish communities, tribes, or petty kingdoms interact with each other and how prevalent was interaction across the Irish sea and beyond. What resources did Irish societies export and import (IE trade) and with whom?
4-how was information transferred in ancient Ireland? Was there a writing system, and if so, what was used to write upon? How were myths, legends and information passed down among the generations?
5-how did culture and religion, as well as their associates practices, differ among the four provinces of Ireland (Ulster, Connacht, Munster, Leinster ), and how severe were these differences?
6-how was war in ancient Ireland fought... what weapons and tactics were used, were there any customs or traditions that were carried out before or after a battle?
7-what kind of cults were found in ancient Ireland, what gods did they honor and how?
8-how does the mythological representation of ancient Ireland compare to its reality? (Do myths like the ulster cycle or the fenian cycle accurately portray ancient Ireland?)
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Ireland at the time you're asking about lacked a written language, though we start to see Ogham developing at the very tail end of this time period, so a lot of the questions you're asking are very difficult to answer with the degree of specificity that can be said of societies that had a rich written record such as Roman or Greek culture. For example we can't really put a name to any gods that might have existed, neither can we say much about battle tactics and traditions as you ask about in question 6. The Romans did write about Ireland but what was written wasn't an "ethnographic" study of Ireland and its people giving us lots of tasty information about specific habits.
On to the questions! Some of your questions contain different parts that overlap (religion, everyday practices) so I'm not going to go down through your question list but rather address the themes I can identify overall. Before I start I need to add that the Iron Age (the period that contains the timespan in your question) has for a long time suffered from a lack of archaeological evidence compared to other periods of Irish history such as the Bronze Age and the medieval period, a recent project by the Discovery Programme (not the TV channel, it's Ireland's nationally funded body for archaeological study) was called Finding an invisible people because so little was known about everyday or vernacular life during this period. To give you an idea of the lack of evidence for settlement, I have read papers published within the last ten years that put out the suggestion that the population may have partially abandoned sedentary agriculture and become wholly or partially nomadic herders, to explain the lack of evidence for houses. The boom of building from the mid-90's to the 2008 financial crash led to a whole lot of archaeological excavation being done so in the last few years we've started to build up a better picture of the Iron Age than could be done pre 2000, but there's a ways to go yet.
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Everyday life, architecture, and agriculture:
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I'm going to talk about these things together because I think they very handily come under the umbrella of 'everyday life' for most people living in Ireland at the time.
Evidence for houses has only really started to come to light in the last two decades or so with the publication of excavation reports from construction-led archaeological works since the mid 1990's. As in Britain, structures both large and small are almost always round, usually post-built, with a central hearth. This represents a continuation of the style of building since the Neolithic. The settlements themselves usually number only a few buildings, unlike in Britain and the continent, we don't get the movement in Ireland towards the development of large, populous 'urban areas' like the Oppida of France or in the Southern British hillfort tradition. On the continent in particular some of these centres had populations in the thousands and were the locations of metalworking and other craftworking on an almost industrial scale.
At this time in Ireland we do get a continuation from the Bronze Age of the hillfort tradition, these are hilltops which have been 'fortified' by the construction of an enclosure, usually of earth. What the exact function of these sites was is not entirely clear; they do not have many more houses than a normal settlement enclosed within them, and as such they may not have been primarily defensive, but the residence of a powerful local person/group, literally elevating themselves above everyone else with the ditches and banks showing off just how much work they could extract from the people under their control. However, these sites do not appear to have much more material wealth than other more low-altitude settlements, as such it has been put forward that they might have had religious or ritual purposes, or been the focal point of the community, a place for meetings, exchange or trade, equally they could have been some or all of these things at once, because of their locations very few have had the need to be excavated.
On to agriculture (and the environment more generally), we know from pollen analysis that at the end of the Bronze Age/beginning of the Iron Age (around 700 BC) many parts of Ireland see an upturn in forest and a downturn in plant species that indicate an open landscape. This is linked to a drop in population and probably part of the reason why this period in history is very poorly understood. However, at the beginning of the time period you're asking about, the pollen record starts showing that things are looking up; the landscape is less dominated by woodland species and open grassland species are making a comeback, along with greater pollen evidence for arable agriculture. For example, at Oldcroghan bog in Co. Offaly, in the centre of Ireland, at around 270 BC woodland in the area recedes and wheat pollen appears. Around this time a knew type of quern appears in the archaeological record; the rotary beehive quern, this is a somewhat more technologically advanced grain-grinding piece of kit than the earlier saddle quern, it was probably introduced to Ireland via Britain from the Continent.
We also have evidence for pastoral agriculture in the form of Cattle and pigs. Some evidence suggests that grains and other plant foods dominated in the spring and summer months with meat being more commonly eaten in the winter, though for most people meat was probably eaten rarely, with dairying being the more common use for cattle than beef.
For everyday people we unfortunately don't have much evidence of recreational activities without a written record. Much time would obviously have been spent farming and maintaining the farm buildings; being made of organic material we know from experimental reconstructions that they decay over the course of about 20-30 years. A later early medieval roundhouse at deer park farms shows evidence of being pulled down and rebuilt in the same spot 5 or 6 times. Labour was also collectively directed towards the creation of things like the aforementioned hillfort enclosures, but also towards other projects like the bog trackways we find in places like Corlea in Longford, demonstrating that long distance travel was important enough for 'roadworks' to be undertaken to traverse dangerous bogland.