What is xenon oxytetrafluoride used for?

In XeF2 the central atom xenon is attached to two fluorine atoms through two sigma bonds and it contains three lone electron pairs. So, steric number = number of sigma bonds + number of lone electron pairs = 2 + 3 = 5. Steric number 5 indicates the hybridization of Xe atom will be sp3d and electron pair geometry is trigonal bipyramidal. Two F atoms are placed in axial positions and three lone pairs are directed towards three equatorial positions. So, the molecule is linear in shape.

Stable in comparison to what? XeF2 is unstable toward moisture, and decomposes both photochemically and thermally. But, according to an article published in 1972, it is more thermodynamically stable than Xe + F2.

It also forms pretty crystals, which is more stable than a lot of compounds.

Your question appears to be how it can exist at all, and the short answer to that is that the octet rule is not the be-all and end-all of chemistry. It’s a guideline that works in the vast majority of organic compounds, and in a substantial number of simple inorganic compounds that involve only non-metals.

Chemically, xenon is pretty happy on its own, but it will combine with elements that are reactive enough to strip electrons away from it: fluorine and oxygen.

Straight from Wikipedia (I can’t remember all the weird compounds like these, sorry about that): there is a handful of xenon fluorides out there.

Three fluorides of xenon are known: the difluoride XeF₂ (XeF2), the tetrafluoride XeF₄ (XeF4), and the hexafluoride XeF₆ (XeF6). These are the starting points for the synthesis of almost all xenon compounds.

The solid, crystalline difluoride XeF₂ is formed when a mixture of F₂ and Xe gases is exposed to ultraviolet light. The ultraviolet component of ordinary daylight is sufficient. Long-term heating of XeF₂ at high temperatures under an NiF₂ catalyst yields XeF₆. Pyrolysis of XeF₆ in the presence of NaF yields high-purity XeF₄.

The simplest explanation for the instability of XeF₃ is that it is a free radical. If you could form XeF₃ it would immediately decompose (disproportionate) into XeF₄ and XeF₂ since both of those two compounds are more stable than XeF₃.

It's just “Xe”. Just the first two letters of the word. Just like how most of the elements of the periodic table are symbolised.We have many exceptions though, just not this one

I hope this answers your question

As far as I know, Xenon Tetrafluoride (XeF4) has no actual use except for research purposes. The interesting thing about this compound is that Xenon is an inert gas which used to mean that it won't react and thus form compounds. But at some point it was discovered that it can make hexafluoride. From there, they found it also makes difluoride, tetrafluoride, hydrate, deuterate, sodium perxenate, and trioxide. Here are some things about XeF4 that maybe you can use and maybe from there, come up with some possible uses:
The process of reacting Xe and F2 in 1:2 ratio is exothermic, and releases 251 kJ per mol.
It sublimes at a temperature of 115.7°C at standard pressure.
XeF4 is a colorless crystal.
XeF4 is stable at room temperature.
XeF4 is exergonic.
XeF4 reacts readily with water, even from the air.

Pretty sure nothing other than proving how badass the chemists who made it are. OK, it also allows us to test our theories of how molecules should behave, since it’s a pretty unusual molecule. But basically, it’s used for research, and nothing else.

Xenon exists in the atmosphere at about 87 parts per billion. As an unreactive noble gas, it doesn't form compounds and so cannot be liberated from other sources. It is separated from the air by fractional distillation; it is found as an impurity in the liquid oxygen fraction when air is condensed and distilled in to liquid nitrogen and liquid oxygen. Additional distillation of the liquid oxygen can separate out the xenon.