Should I apply 5% Minoxidil only to the areas very affected by thinning (i.e.: temples)? Or the whole scalp?

Minoxidil, which is felt to increase blood flow to areas where it is used, should be applied to the areas where hair loss is present.  It won't be beneficial being placed in areas where there is no current loss.

While minoxidil works for some, the problem with the medicine is that
it does not stop hair loss, and the DHT will continue is binding to the
hair shaft which will eventually overtake any additional growth caused
by the Minoxidil and die, perhaps just slightly later than it would have
without the medicine.
Also, the alcohol base required to support the active ingredients
also cause irritation of the scalp and severe reactions for many people,
such as the increased shedding you are describing. The fact is that it
does not work for everyone.
The number one first step I recommend is a comprehensive consultation
with a hair regrowth specialist who will perform lab tests to determine
the underlying cause of your thinning. Without labs, no-one can really
know what your true cause is and any treatment will be temporary at
best. From here, you can receive the best treatment for your case. 
It is also worth noting that any medicine that actually can make
changes inside your body, are required under the FDA to be available by
prescription only. This therefore means that it is not possible for
anything that does not require a prescription to cure or prevent hair
loss or regrow thinning hair. Thus, a personalized medicine will be the
best choice because instead of a "one size fits all" approach, you will
be taking something which is truly catered to your body's needs.

The treatment is out there. Good luck on your search.

Minoxidil should be applied to the area where you believe it is needed. If you place it all over your scalp, for example, you will absorb more of the drug into your blood stream