It's important to distinguish between the general idea and how it was accomplished. There might be ways for instantaneous transport without dematerializing and rematerializing an object. We might discover a quite novel way to do a lot of the things depicted. So far we've recreated a lot of magic from ancient stories with technology, we'll probably do the same with a lot of the things we see in Star Trek. And we probably won't be to able to guess which ones, nor how.
Faster than light travel – highly unlikely. Current theories don't say that FTL travel is impossible. They just say that an object having a velocity bigger or equal to lightspeed is impossible and requires infinite energy. The velocity of objects travelling in a warp field or through a wormhole doesn't exceed lightspeed. No current laws of physics broken there. Well, the second law of thermodynamics and causality will be broken, but only to the extend that with the introduction of wormholes we no longer have a system where they apply globally (not to mention that both are currently tested only at locally anyway).
If faster than light travel is possible then so is time travel, and since I think time travel is impossible, so is faster than light travel.
Time travel – highly unlikely. Like FTL travel, it doesn't violate any physical laws. However, the possibility of time travel would carry many implications that are a bit too large to assume that it is likely. It would imply that time isn't linear, that the past still exists at some form and you can look into it or go there. It also creates a numerous paradoxes. They are easily resolvable but the problem is that all resolutions are insane.
Faster than light communication – same as above. With a note, quantum entanglement doesn't allow faster than light communication, and is unlikely to ever will, and if you do you'd have to rewrite the entire quantum mechanics.
Communicators – parts already here, parts highly unlikely. They include FTL communication, and that part is impossible. Sending signals that can reach everyone on the entire planet seems unlikely, but with a power source big enough and sending a directed signal after the initial handshake it might work. But they will likely be illegal and/or dangerous, and they'll interfere with each other if too many people have
them. Also, current low frequency transceivers that are good approach for handling this problem, and they need big antennas.
Tricorder – parts already here, the interesting parts highly unlikely. Well, it's just a computer that makes passive and active scans. We already have those, and we'll improve them. The problem is that they find information that simply isn't there and isn't acquirable. You can't detect a person walking behind a wall for all that I know, even with an active scan. You can't go that much further than what you can see with your eyes. The part that they can interface with any computing device and do crazy stuff is also impossible.
Medical tricorder/scanners – yes. Fortunately, some wavelengths pass through human tissue, so these are entirely possible. We just need a few advances in artificial intelligence.
Interactive computers – unlikely. We will probably develop the technology, but this is an incredibly inefficient and uncomfortable interface. It just won't fly. It might work for pocket computers, though. By the way, artificial intelligence is very far from achieving that kind of sophistication. I even think that it's going in the wrong direction. I don't except the technology in less than 50-100 years.
Androids – of course. We'll have real androids as soon as we get real artificial intelligence. And we'll have androids as intelligent as my ex in 10-20 years.
Phasers – well, laser weapons, yes. Won't be anything like their TV counterpart, but they will be here. They just need nuclear energy cells or something. I imagine them firing an invisible and silent but lethal laser beam. You just press a button on a device, and magically a person on the other side of the street gets a huge injury.
I don't know about the stun setting, and if that one is possible, but you can certainly cause the target 1st degree burns if you wanted. That might cause them enough pain to stop them them from whatever they were doing. It would be dangerous to the eyes, though.
Sonic disruptors – as a device that knocks you on the ground, yes. As a device that kills, I hope not.
Transporters – highly unlikely. We might be able to do something similar with single particles very soon. However, transporting entire objects separating them from their environment is a task so big that I can't even think about it.
However, while we are rewriting the laws of quantum mechanics for the FTL communication above, we might find other ways to do it. You just have to make the atoms think that they are where you want to transport them, and they will be there. Or you might create a mini wormhole and make the body fall through it. Or you might change the notions of the geometry of space and go around the wall of a completely enclosed space.
Forcefields – likely, but probably not as they are shown.
Suspended animation – yes. But I have a feeling that the process will be too intrusive for the body, and people are unlikely to want to go ahead with it.
Mating between different species not from the same family – no.
Artificial gravity – we already have it. But it's a bit expensive and requires massive spacecrafts. Now, if you can create gravitational radiation, you might have a direct approach. I find this not very likely, but not impossible either.
Holodecks – yes. Different technology, of course. I think that neural interface will be the common way, but normal holograms would also exist. They might be able to interact with objects, too.
Tractor beams, holograms that can touch you – no and yes. Unlikely in the form they were shown, but you can create technology that exerts forces on objects and you might use it to construct something that works similar in some of the situations. But the nature of the objects is important. You might have medical holograms, but they can only utilize equipment designed for the use of a hologram. No holographic lungs, though.
Accessing minds through technology - unfortunately, yes. It's only a matter of time. But you won't be able to read them like a book. Brains allow only active access. Like smart cards, it would be hard to read them if the card doesn't cooperate.
Using neural interface to control computers, implants, artificial libs and stuff – yes. We can already control our own limbs which are a kind of machines. So we can use construct other machines that we can control too. And the brain is very clever at interfacing with anything. But you might have to do it at early age.
Universal translator – yes, no and no. Translating, yes. Learning languages automatically, yes. Seamless translation, no. Learning almost any language automatically without external aid, no. Doing it in a blink of an eye, no. And everyone who needs to understand the foreign languages will have to carry them.
