Chemistry - Arrows used in chemical reactions

Solution 1:

The second one, $(2)$, $\ce{<->}$, indicates resonance structures.

The difference between the second two is explained in another post -

What are the correct equilibrium arrows?

Loong basically says that $\ce{<-->}$, $(4)$, indicates forward and reverse elementary steps happening in equilibrium, that is that those are the only two things actually reacting with each other. On the other hand, $\ce{<=>}$, $(3)$, indicates a net reaction, that is that there may be multiple steps in between, leading to this net equation. He does a more in depth explanation of this in his post.

Case $(5)$ indicates a net equilibrium where products are favored, and $(6)$ indicates a net equilibrium where reactants are favored.

Solution 2:

The IUPAC Green Book (Quantities, Units and Symbols in Physical Chemistry, Third Edition, 2007) reads:

2.10.1 Other symbols and conventions in chemistry
[...]
(iv) Equations for chemical reactions

(a) On a microscopic level the reaction equation represents an elementary reaction [...] A single arrow is used to connect reactants and products in an elementary reaction. An equal sign is used for the "net" reaction, the result of a set of elementary reactions. [...]

$\ce{H + Br2 -> HBr + Br} \quad$ one elementary step in HBr formation

$\ce{H2 + Br2 = 2 HBr} \quad$ the sum of several such elementary steps

(b) On a macroscopic level, different symbols are used connecting the reactants and products in the reaction equation, with the following meanings:

$\ce{H2 + Br2 = 2 HBr}\quad$ stoichiometric equation

$\ce{H2 + Br2 -> 2 HBr}\quad$ net forward reaction

$\ce{H2 + Br2 <--> 2 HBr}\quad$ reaction, both directions

$\ce{H2 + Br2 <=> 2 HBr}\quad$ equilibrium

The two-sided arrow $\ce{<->}$ should not be used for reactions to avoid confusion with resonance structures [...]

2.12.1 Other symbols, terms, and conventions used in chemical kinetics
[...]
(ii) Composite mechanisms
A reaction that involves more than one elementary reaction is said to occur by a composite mechanism. The terms complex mechanism, indirect mechanism, and stepwise mechanism are also commonly used. Special types of mechanisms include chain-reaction mechanisms, catalytic reaction mechanisms, etc.

Examples
A simple mechanism is composed of forward and reverse reactions $\quad\quad\quad\quad\quad\quad\ce{A -> B + C}$
$\quad\quad\quad\quad\ce{B + C -> A}$
It is in this particular case conventional to write these in one line
$\quad\quad\quad\quad\quad\quad\ce{A <--> B + C}$

However, it is useful in kinetics to distinguish this from a net reaction, which is written either with two one-sided arrows or an "equal" sign
$\quad\quad\ce{A <=> B + C}$
$\quad\quad\ce{A = B + C}$

When one combines a composite mechanism to obtain a net reaction, one should not use the simple arrow in the resulting equation.
$\quad$Example $$\begin{align} \ce{A &\to B + C}\quad\text{ unimolecular elementary reaction} \\ \ce{B + C &\to D +E}\quad\text{ bimolecular elementary reaction} \\ \hline \ce{A &= D + E}\quad\text{net reaction (no elementary reaction,no molecularity)} \end{align}$$

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The ACS Style Guide reads:

Many kinds and combinations of arrows can be used. For example, two full arrows in opposite directions ($\ce{<-->}$) indicate a reaction that is proceeding in both directions. Two arrows with half heads in opposite directions ($\ce{<=>}$) indicate a reaction in equilibrium. A single arrow with heads on both sides ($\ce{<->}$) indicates resonance structures, not a reaction.