Fundamentals of atomic bonding Are these basic statements about atoms and bonding correct:  


*

*atoms are at their lowest energy state when they have no bonds, existing as single atoms  

*it always requires energy to form any molecule from two or more individual atoms  

*when individual atoms bond to form a molecule entropy always decreases and stored chemical energy always increases

 A: All of those statements are false, and counterexamples are common.

atoms are at their lowest energy state when they have no bonds, existing as single atoms

The energy state of a molecule in its ground state is frequently lower than the energy of all of its constituent atoms in their ground state. For example, water has less total energy than two isolated hydrogen atoms and one isolated oxygen atom.

it always requires energy to form any molecule from two or more individual atoms 

Atomic hydrogen forms at high temperatures and will condense to molecular hydrogen if you cool it down. That is removing energy.

when individual atoms bond to form a molecule entropy always decreases and stored chemical energy always increases

Total entropy never (or almost never, it's a statistical law) decreases. Stored chemical energy frequently decreases too.
A: 
atoms are at their lowest energy state when they have no bonds,
  existing as single atoms

Atoms are at their lowest (electronic) energy state when they are not excited or ionized. A molecule can also be in an excited, ionized or a lowest state, depending on the situation. 

it always requires energy to form any molecule from two or more individual atoms

No. You cannot say "always". There are some atoms in nature, such as O, N and H that are so reactive that they do not exists as free atoms but always in some form of molecule.
But there is one thing to keep in mind that is in general some energy is required for a chemical reaction to occur. This energy is called the activation energy. There are many chemical reactions for which the activation energies are so small that in normal conditions the reaction occurs itself.  
