Astrophysics student here. If you are interested in finding out the practicality of future technology I suggest you read Michio Kaku The Science of the Impossible (also a TV show (sci fi Science) but i cant speak to its quality as i haven't seen it.)
FTL in science fiction is based off the idea that its technically not impossible, just very very hard. The Wormholes are the most scientifically sound forms of travel as there are technically ways to make a wormhole traversable but we dont know how. Warp drive is also very likely. scientists are working on ways to bend space time around ships that will allow them to glide through space shortening the distance between places. The problem with these theories is that they require either extremely large amounts of energy or require the existence of exotic matter which as of yet is not discovered. The least realistic possible way is the Hyperlanes which exists in many permutations across sci fi titles. In star wars its hyperlanes, in warhammer 40k there is a version as the webway. this is the idea that there are regions of space that are some how folds in space time that allow ships to traverse at FTL speeds. ( they could maybe but not likely exist but the cost at maintaining them would be immense and a species would be better off finding another version of ftl travel)
In Michio Kaku's book the physics of the impossible (which is easy enough for the layman to understand, so i suggest everyone interested in sci fi read it.) he classifies technology as having 3 different levels of impossibility.
Class 1 impossiblities are force fields, invisibility, phasers, teleportation, telepathy, psychokinesis, robots, ETs, starships, and anti matter / anti- universes.
these are things that impossible for us today, but they dont actually violate any known or set laws of the universe. The key to these types of technologies or discoveries is that as of right now we really dont know how to find them or build them without using exorbitant amounts of power. the idea here is that they technically can exist as long as we aren't tied to the way that they exist in the sci fi media we are used to. example Force fields will likely be a combination of 3 types of tech, magnet fields, laser fields and carbon nanotube wire together these things will likely be able deflect most types of debris or weapons we can envision now. and all exist in a way that can be created in a lab but not to what is required of it in sci fi.
* these kinds of tech are likely to be possible in the next 2 centuries*
Class 2 impossibilities are FTL, Time Travel, and Parallel Universes.
"these are technologies that sit at the very edge of our understandnig of the physical world. if they are possible at all, they might be realized on a scale of milleninia to millions of years in the future..." Except from physics of the impossible preface
Class 3 Impossibilities are perpetual motion machines and precognition
"these are technologies that violate the known laws of physics. surprisingly there are very few such impossible technologies. if they do turn out to be possible, they would represent a fundamental shift in our understanding of physics" Except from physics of the impossible preface
Time dilation is another subject and I'm not proficient enough to explain it here. the essence really boils down to what time is. this is a question that is way more complex that the simple answer most people give. and it would be easy to spend many lectures just on this subject. but the basics of it is that as you approach the speed of light you are traveling at a different speed time wise compared to others (you are technically in a different time zone) we actually have problems with satellites in space getting desynchronized from us down here because time is different up there. (due to gravity) There are really easy ways to search for this on youtube.
(side note ) What I'm most excited in is the fermi paradox and the discovery of intelligent life in the galaxy. Kurzgesagt did a fantastic 2 part video on this. its relatively easy to find on youtube. (and they also have a fantastic video on the possible deaths of the universe. ) The idea of so many species in the galaxy all having tech is harder for me to wrap around than the FTL in this game. I also have a bad habit of looking at stuff and deconstructing how they look and yelling in my head that "THATS NOT HOW IT WOULD LOOK/WORK!!!" but if anything I am a fan of the possibilities presented sci fi.
Arthur C Clarkes three laws
Clarke's first law
When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.
Clarke's second law
The only way of discovering the limits of the possible is to venture a little way past them into the impossible.
Clarke's third law
Any sufficiently advanced technology is indistinguishable from magic.