Oooookaaaayyyy...
I'm not exactly a physicist but as my old dad would say, I have just about enough knowledge and understanding to be dangerous.
so let's take a crack at this. Also Sorry this could get quite long winded, that's a lot of questions.
We should probably preface this by saying that light is composed of particles called photons, these are odd little things in that they behave as both a particle and a wave and depending on the circumstance and the effect being observed determines which form you are measuring it in.
For the first part of this you need to know a little bit about absorption, light absorption is a process by which light is absorbed and converted into energy, Just like in photosynthesis but it can happen to all objects not just plants. It depends on the electromagnetic frequency of the light and the vibrational frequency of the electrons in the atoms of the object. When the two are complimentary the light
particles are absorbed, if they are not complimentary then light either passes through or is reflected off (as would be seen by a
wave).
The law of conservation says that energy cannot be created or destroyed only converted from one form to another, so when light particles are absorbed their energy is converted into heat (this is why things get hot when left in the sun and the principle behind solar panels)
You would normally witness both possibilities happen at the same time to some degree unless the light in question is highly controlled to produce a very specific frequency, for instance sunlight is composed of lights of various frequencies from 400 - 800 nanometers (more on this when we get to refraction).
So with your torch on there is a continuous supply of photons being emitted, these will fly out and collide with any objects in their path, some of them will be absorbed and converted to heat and some will be reflected losing a little energy as heat in the process and changing the frequency.
However when you turn the torch off that unending source of photons is removed and any that already exist will continue bouncing around being absorbed and reflecting off of any objects in their path until they are all completely absorbed. Now remember how fast light travels? well at that speed it is a tiny fraction of a second until all the photons your little torch was able to create have been completely absorbed (about 1 millionth of a second).
Interestingly, in space this is a little different see, because space is actually pretty empty. There is bugger all up there for the photons to bounce off of and therefore not a lot to absorb them. So in this case they just keep on going until they do hit something and either get absorbed or reflected to travel on some more.
In the case of shadows or inside boxes, Light photons travel in straight lines, whatever direction they are moving in they will stick to without turning or cornering. Until they are absorbed or encounter an object that they either reflect off of (at which point the angle of incidence equals the angle they reflect off to and continue in that line) or they encounter and object that refracts them.
Refraction is the change of a photons direction when it passes from one medium to another with a different density that changes it's wave velocity.
This is most commonly seen when you put a straw in a glass of water and it looks bent at a different angle. Light as a wave is passing from air into water changing its velocity and therefore its direction.
This is also why the many frequencies in sunlight through a prism or reflecting off a CD comes out as a rainbow, the prism/CD refracts the different frequencies of light at different angles breaking it into visible colours but it will also absorb some of the particles as well.
Because as an object increases in speed it is the mass that increases.
Mass and size are two entirely different things, the types of atoms an object is made of and their density determines its mass.
A balloon filled with helium will have less mass than a balloon the exact same size filled with water which in turn will have less mass than another same sized balloon filled with gold.
The three balloons may be the same size but the atoms they are filled with and the density of them is totally different for all 3.
They are often confused and thought to be the same because if the size increases the mass does as well because there is now more space and more material. But mass can increase without a corresponding size increase.
The confusion goes back to badly described terms when these theories were originated, modern physicists now tend to use the term Kinetic Energy or Inertial Mass to differentiate between an objects resting mass (it's mass with 0 speed) and it's potential mass when accelerated to higher speeds.
In physics mass in speed equations is simply locked up energy, the more modern terms of kinetic energy or inertial mass is the amount of resistance an object has to a change in its motion (for instance acceleration or change in direction). When they say an object's mass increases they mean its inertial mass.
Actually some light does bounce off the magnifying glass (hence why you might see a little white spot on the glass itself) and some light will also pass through a plum blossom, as well as being absorbed by traveling through and relfecting off of both, all due to containing many frequencies at once.
I really can't get into the whole time thing, it is quite a complicated topic to explain easily and there are a lot of weird phenomena around it, depending on who is observing and where they are observing from in relation to the object in motion. However that is actually backwards time moves faster the further you get from the planet, at least from certain frames of reference.
edited to add that if you'd really like to discuss this more PM me as I 'm overtaking a fun thread here.
and a Genie popped out and shouted "I will grant everyone 1 wish ! All they need to do is answer this thread starting with "I wish I wish I wish." 
..and two collie dogs 
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