Yes, every rank is a single +1 to the skill
Diminishing returns are handled by increasing the cost per skill rank as you increase ranks in the skill
As for where it is stated....... I MAY have made one of those critical errors of not explicitly stating something that I had previously thought was obvious. Unfortunately that happens sometimes....
However, it is kinda stated/implied in some places
For example, the last paragraph of the left column on page 16 says:
The second element is the Stat Bonus. This number is
determined by your Stat Value (see below). It is added to
your skill ranks to give you your total skill bonus and is also
used for other things, such as Saving Throws (p. 84).
The important part is bold and maroon...