On page 12 the rule is introduced that fractions are always rounded up.

So is the following assumption correct:

-Tim shoots sniper rifle using 1AP for the attack scoring 5 DoS

- The fowl rodent evades with 2 DoS

Thus 2 DoS is scored by Tim. The RoF or RoA is 1/3 but as its a fraction it counts as one and hence Tim successfully hits the bunny once..

Correct or not?

Sadly it is not. The equipment section regarding RoF clearly states that RoF is one of the few things that doesn't round like that.

p. 132

"Some weapons have a rate of fire that is a fraction such
as “1/2,” “1/3,” or “1/4.” In these cases, these weapons
cannot be fired unless the action being used to attack
multiplies their RoF above 1."

To further clarify, in order to attack with a weapon, you must spend a number of

Action points that bring the rate of attack to at least one. The rate of fire shows how much a single action point gets you (sniper rifle is RoF 1/3, takes three action points to reach a rate of attack of one). Degrees of success on an attack roll DO NOT increase its rate of fire. Instead, the rate of attack determines how many degrees of success can be counted as a successful hit. Evasion decreasing the degrees of success on an attack roll does not decrease the rate of attack paid for by action points.

In your example, Tim would pay at least 3 action points to fire his rifle at a rate of attack of 1. However, as KommissarK said, RoF does not round up, and time could not get a rate of attack of one by only paying one or two action points, not could be get a rate of attack of 2 by paying 4 points. Tim's roll succeeds, and since his RoA is 1, he could only get one hit. The rodent evades with 2 DoS. (In your example, if Tim had 5 DoS and the rodent scored 2, Tim's DoS would decrease to 3, not 2), but Tim still has at least one DoS, which is all his rate of attack of 1 can use anyway. Tim hits the rodent.

Thanks for the clarification.