v>c is not allowed, but v here is the speed of anything from the point of view of something else in an inertial frame of reference. And "speed" is defined something like "if this thing was a mirror, and I sent two light pulses towards it 1s apart, how far apart would I see reflections of it". In a similar way "time" is defined as "if this thing was two mirrors 1 light-second apart, with light bouncing between them, how long does it take a photon to bounce from one mirror to the other and back". You can picture why there is time dilation if you imagine the two mirrors moving, and the light bouncing diagonally between them. Because of geometry the diagonal path is longer than a straight path—this is where all the square roots in the formulae come from—, but the speed of light is fixed, so "time" stretches out. These geometric definitions sound pedantic but they are actually useful and accurate with respect to the more formal definition that uses a non-euclidean metric space.

If you instead define "fast" from your own point of view, as in "how far away it is / how long it would take you to reach it", then you can be arbitrarily "fast".

The loophole is space contraction / time dilation: you will never see the speed of your destination be higher than c as long as you are in an inertial frame of reference, that is, not accelerating. But as you accelerate you'll find all distances between all objects become less than they used to be before you started accelerating. So the apparent speed of your destination will be

v_apparent = v_inertial + Δγ/Δt * d.

Since Δγ/Δt depends only on your rocket, v_apparent can be arbitrarily large.

So in the middle of your trip towards Andromeda, 14 years after you departed, from the point of view of the Earth you will look like a compressed, redshifted blob moving at almost the speed of light, that left 100000 years ago and still has 100000 years to go.

From your point of view, the Earth below looks like a compressed, redshifted blob approximately 1 lightyear away. It is vertically mushed together along with most of the Milky Way. Andromeda is also approximately 1 light year away and looks compressed and blueshifted.

From the point of view of your destination in Andromeda, 14 years ago a relatively bright, blueshifted thing came out of the Milky way and has already moved halfway across. In 14 more years it will arrive. If you defined speed as apparent distance / apparent time it'd look like you're moving faster than light, but if Andromedans know about the speed of light, they'd know you're not actually moving faster than light.

You can't actually see coming something that moves faster than light. If you were, when you arrived you could look behind you and see yourself from the past, moving backwards as the light from your ship arrives after you did.