Step 1: Check statement (i).
When a charge speeds up or slows down, it makes changing electric and magnetic fields that travel out as a wave. So accelerating charges do produce electromagnetic waves. Statement (i) is correct.
Step 2: Check statement (ii).
An electromagnetic wave carries energy and momentum across space, but it does not carry any net electric charge with it. So statement (ii) is correct.
Step 3: Check statement (iii).
In an electromagnetic wave the energy is split evenly, with the electric field holding the same energy as the magnetic field. Statement (iii) is correct.
Step 4: Check statement (iv).
The speed of these waves changes from one medium to another. It is fastest in vacuum at $c = 3\times10^{8}$ m/s and slower in glass or water. So statement (iv) is wrong.
Step 5: Collect the correct ones.
Statements (i), (ii) and (iii) are correct, while (iv) is not.
Step 6: Choose the option.
\[ \boxed{(i),(ii),(iii)\text{ only}} \]