There are three ways to accounts for similarities in folklore, religion, etc.
The first is diffusion. Oral tradition by its nature diffuses, and so motifs are frequently shared internationally. This accounts for some of the perceived similarities, but where there is no obvious historical connection, other reasons need to be considered.
The second reason is the shared human experience. We all live in the same world with many of the same organisms - at least generically. And we share the same laws of physics and an earth that behaves in much the same way internationally. Besides all that, people are people; despite dramatic cultural differences, there is a great deal that unites us in our perception of reality - birth, death, eating, sex, etc. Because of this wide range of similar experiences, folklore and belief systems can seem to have a great deal in common.
The third factor to consider is that people are inclined to see patterns - even when none exist. Some stories and motifs seem to be similar internationally, but when looked at carefully, it often become apparent that there are more differences then similarities. Beware the illusion of similarities when few exist!
Just to expand a bit, in the vein of the excellent and concise answer by /u/itsallfolklore:
Questions like this appear fairly often on AskHistorians. There’s a link in another comment to a discussion of flood myths. Questions on serpent monsters also get asked a fair amount: here’s an exemplary answer from /u/artfulorpheus.
I’m going to take a slightly different approach, however, and lay out a range of approaches that
scholars have taken to this question of similarities among traditional narratives from a variety of cultures. So this answer will be more methodological, but hopefully still useful and interesting!
First, though, some key caveats on the nature of “seeming similar.” While fascinating links can indeed be made between countless stories from countless cultures, it is important to consider that some stories may appear especially similar because of how we encounter them. Most speakers of modern languages encounter traditional stories in retellings which are themselves based on translated sources. Translation goes a long way towards “taming” difference. This is particularly true of the types of supernatural beings and concepts that tend to abound in mythic narratives. Once you start calling a monster a “dragon”—regardless of whether the original source called it drakōn, tannīn, wyrm, azhdahā, lóng, etc.—you’ve already taken a step towards connecting distinct motifs that may have important, culturally-specific valences which become lost in translation.
This is then compounded by retelling and adaptation. Not only do retellings often smooth over difficulties and discrepancies in source texts, they also carry with them the biases of the reteller. The reteller may have a specific agenda, or may (consciously or not!) be importing tropes and storytelling patterns from their own era or culture. An anthology that groups myths, as many do, by theme--Creation Myths, for instance--automatically provides a lens that affects our readings of the myths in that section. This lens can be enlightening, but it can also introduce distortion. Nor is this distortion unique to the modern period. There’s been a lot of good AskHistorians discussion about Norse mythology (like this from /u/Platypuskeeper), and how difficult it is to establish what these stories might have looked like in pagan times--given that all our surviving written sources were composed by Christians, living in a densely interconnected medieval Europe.
All of which is just to say, that good comparative mythology is difficult work. It requires careful readings of difficult texts in their original, often-difficult languages, and a thorough knowledge of the contexts--manuscript/codicological, historical, sociocultural, etc.--under which these sources were produced. But even that is still only just the beginning, because the challenge remains of how to account for the types of similarity that your question mentions. In what follows, I’m going to outline an array of the most common methods for analyzing these links. This isn’t exhaustive--there are almost as many comparative methodologies as there are comparatists--but I hope it provides a sense of some widespread approaches.
One of the most enduring and tantalizing is the notion that stories are similar because they derive from a common original source. Perhaps this is an ur-culture, which disseminated its beliefs and stories widely through conquest or other forms of dominance; perhaps a particular event (this pops up every now and then in news stories reporting that a particular flood identified by archaeologists or geologists is the flood described by sources like the Bible). For more recent tales, it might even be a particular text that became widely shared, translated, and retold. Common origin is appealing because, in theory, it should be provable--we should be able to trace lines of transmission back, link by link, to a point at which they converge upon a single source.
The quintessential ur-culture are those Indo-Europeans, who are often claimed as the progenitors of a significant amount of Eurasian traditional narrative. Since comparative philology established that languages like Sanskrit, Armenian, Greek, and Irish all evolved from a common ancestor, many comparative mythologists became intrigued by the idea that the stories told in this ancestral tongue may have followed a parallel pattern of dispersal and evolution. This, they posit, may account for similarities between stories like the Persian legend of Rostam and Sohrāb, the Irish Aided Óenfhir Aífe, and the Germanic Hildebrandslied, which all tell of a fatal incognito battle between a father and his son. Epitomes of this type of scholarship are Calvert Watkins How to Kill a Dragon (1995; less practical than the title suggests, unfortunately), and M. L. West’s Indo-European Poetry and Myth (2007). These are largely unimpeachable philologically, and contain a lot of interesting material. But problems remain. The hypothetical common original is still just hypothetical; and it’s worth asking exactly how useful it is to point out that the Avestan hymns of the 2nd millennium BCE (?) and the Old Norse Eddas of the 13th century CE were both written in languages ultimately deriving from Proto-Indo-European, given how different their contexts otherwise are. This is even leaving aside the issues of dubious race science and ethnonationalism, which have plagued Indo-European Studies from the start; and, for some, essentially damn the entire project. Stefan Arvidsson’s Aryan Idols (2000) is a good overview of this critique, though a lot has happened in the intervening 20 years. More recent--if focused in a slightly different direction--is Stephanie von Schnurbein’s Norse Revival (2016).
For some tales, however, there are fairly good documentary trails. As European traders and missionaries became more familiar with Indian culture in the Early Modern period, they were surprised at how similar their hagiographical story of Barlaam and Josaphat was to the Buddhist account of Siddhartha’s encounter with the “four sights” that led him to a realization of impermanence and, eventually, enlightenment. Subsequent scholarship has established pretty conclusively that the Buddhist legend traveled from India to Persia and Central Asia, on into the Middle East and Anatolia, and then throughout Europe, changing languages and ideological affiliations along the way. While there are a handful of important cases like this, many other more tenuous borrowings have been proposed. It’s important to evaluate these kind of claims carefully. There’s a long history of trying to claim that the Persian Vis o Rāmin is the origin of the European Tristan cycle, but the evidence for this is very weak.
Another important way to think about comparison is through motif-based or tropological approaches. These are often less concerned with origins--so are perhaps more tangential to the question--but can provide a framework for other approaches as well. Among the pioneers of this approach were Russian formalists like Vladimir Propp (Morphology of the Folktale, 1928) and other folklorists like Antti Aarne and Stith Thompson. By exhaustively cataloging motifs across traditional narratives, these scholars provided tools for assessing the relationships among tales. A particularly thick geographical cluster of a particular motif may indicate something about its origin; by contrast, a widely dispersed motif is often harder to trace to any particular culture. Often, though, these methods are more diagnostic than they are explanatory.
(con't)
Though they don't cover all the topics you mention, the answers in this thread from /u/Tiako and myself about ancient flood myths should prove interesting.