Re: Summer T-shirt; is white actually cooler than navy blue?

To answer this question you need to think about both the heating and
cooling processes - which are ultimately going to determine your 
temperature.

On a hot, sunny day generally what is doing most of the heating is the
radiation of the Sun itself.  So, to keep cool you should wear light
coloured clothing, as you suggest.  This very simply acts a like
a mirror, reflecting much of the sunlight, and reducing the amount
you absorb.  Once you are inside, with air-conditioning, any difference
due to colour is likely to be negligible.

(Note in passing; that fully reflective clothing, like some survival
blankets, would be even more effective at reflecting sunlight, although 
may be less appropriate - apart from anything else - if it didn't allow 
your skin to "breath".  Such materials also keep in the infra-red radiation
from your body, which is one cooling mechanism, and hence are most 
valuable when trying to keep warm in cold conditions).

The other side of the "hot day" coin is cooling.  On hot days, the most
important mechanism is sweating - the evaporation of the sweat cools it,
and hence you.  This brings us to your question about humidity, since
the problem on humid days is that the air is so full of moisture that
evaporation is considerably slowed down.  As you probably know from your
own experience (and I should admit that in the UK, we very rarely get
seriously humid weather!), on humid days it can be pretty hard to get any
kind of relief from the heat.  To be honest, I think the only advice
then would be to wear clothes which are as "light" as possible, in the
sense of being thin and loose, thus maximising the contact between skin 
and air.

(Another aside: in some activities, such as mountain climbing, external
conditions may be cold, but exercise tends to make you hot and sweaty.
It can be difficult to regulate temperature, and you want to avoid, for
example, cooling too rapidly when you take a rest break.  One way that
the right clothing can help there is if it draws sweat from your skin
so that it does evaporate, but your skin is not in such direct contact
as the cooling takes place.)

So I think your suggested modification of uniform is a good one - best
of luck in getting it adopted!