Can a free radical be created by chemical reaction of non-radical species? Here's my thinking: 


Atomic oxygen in its ground state is a free radical because there are two unpaired electrons in p-orbitals. 
When species react new orbitals are formed, and perhaps a situation can occur where the amount of degenerate orbitals is changed by a chemical reaction. This would implicate the filling of these orbitals, following the aufbau principle and hunds rule of filling.
Therefore it is thinkable that two reactant species (i.e. not homolytic bond fission) which are not radicals, can react in such a way that the new electron orbitals are filled in such a way that all electrons are no longer paired => radical species formed from non-radical species.
Likewise it is conceivable that a radical species can react with a non-radical species (i.e. not an even number of radical species terminating eachother) to form only non-radical species.


Is my argument and results 3 &amp; 4 correct? Can someone give an example of 3 and/or 4?

Edit: My main takeaway - when considering the feasibility of a radical creation/destruction, look at conservation of spin
As for #3, photoinduced electron transfer (PET) reactions do what you want. 

Imagine that 2,4,6-triphenylpyrylium tetrafluoroborate ($\ce{P+BF4-}$) is irradiated at $\lambda = 350~\mathrm{nm}$ in the presence of an alkene and a nucleophile ($\ce{ROH}$).



In the excited singlet state, $\ce{^1P+^*}$ is a strong electron acceptor, that oxidizes the alkene to the corresponding radical cation an is itself turned to a pyranyl radical, $\ce{P^{\cdot}}$. (Here is the first radical.)

Then the alcohol adds to the alkene radical cation, the adduct deprotonates spontaneously. (Here is the second radical.)