A. true
b. false: a wave can slow down and lose energy even within the same medium.

Wow !  There's a surprising bunch of ambiguities and misconceptions all wrapped up in that short burst of 13 words.

-- A wave doesn't need to slow down in order to lose energy.
-- When a wave loses energy, it doesn't necessarily slow down.
(A huge seismic wave and a gentle ripple both have the same speed
in water.)
(The light from one LED and the light from an exploding supernova
both have the same speed in space or in air.)

-- When you make a wave carry more energy, it doesn't go faster.

-- When you take energy out of a wave, it doesn't go slower.

-- A wave passing from warm air into cold air slows down. 
But it doesn't lose energy until it has gone some distance,
and that's not because its speed changed.

-- As long as it stays in the same medium, a wave doesn't slow down,
even though it may lose energy as it proceeds.

-- A wave's energy doesn't depend on its speed, and its speed
doesn't depend on its energy.

-- A wave's speed depends on the properties of the medium. 
So, technically, as long as it stays in the same medium, its speed
doesn't change, no matter how much energy it's carrying.

-- You may say "Well, I read that light can get slightly faster and slightly slower
in air, and in fact, the change of speed in air is responsible for the refraction of
light in air."

My answer to that is "Yeah but."

Light can slightly change speed in air, but that's because the properties
of the air have slightly changed.  So it seems to me that you'd have to say
that the air became a slightly different medium.

Have I missed any major permutations.

U okay bro