if power is increased during a turn while maintaining a constant angle of attack - the rate of turn will decrease and the radius of turn will increase because if the power is increased then the speed will increase as well.
I don't have Bob's book so I will talk a bit generically.
It gets a little messy as the power increase (actually, we are interested in the thrust increase associated with the power increase) can go towards increasing speed and/or providing for an increase in climb performance if you manage to maintain a constant alpha. I presume that the inference in Bob's text is that the turn is undertaken while maintaining a constant height ? In this case you would expect to see a speed increase. Radius of turn increases at a modestly higher speed while turn rate will reduce due to the larger turn radius.
if power is increased during a turn while maintaining the stalling angle of attack the radius of the turn will remain the same, and the rate of turn will increase.
I suspect that you may have misread/misquoted the text here as the statement doesn't make a lot of physical sense.
Aside - another relevant term you may see is "cornering speed", especially in military parlance. This is where you are simultaneously at the maximum g load permitted and at the stall speed for the gross weight (if you can generate enough thrust to do this - generally only applicable for high performance fast jets) which gives you maximum turn performance for the aircraft. The operative consideration is thrust, rather than power.
At a high alpha (angle of attack) - we are talking stall angle, here - the thrust line provides a measurable component of that thrust towards the centre of the turn. Think back to any military fast jet airshow display you have seen - the jet will be in afterburner to maximise the thrust output. This has the effect of providing an additional force (centripetal force) toward to the centre of the turn which has much the same effect as increasing the wing lift component and you end up with a reduction in turn radius. Recall from elsewhere in your texts that it is the centripetal force which is causing the turn.
A similar observation applies to looping manoeuvres - the jet in A/B at high alpha is able to perform a considerably tighter loop than without A/B for the same conditions. I still well recall an ARDU Mirage display at Ballarat (if my memory is correct) about 40 years or so ago. The pilot came in over the runway at low level and then proceeded to do several loops up into the cloud base and bottoming out at probably only 30-40 feet above the runway - eye opening stuff, indeed !
A similar concept in civil aircraft is the minimum value for the design Va, which is the same intersection on the VG envelope at MTOW. The light aircraft, however, doesn't have anything like enough thrust to manoeuvre at this point. Keep in mind that Va is not driven by this observation, but is a consideration for the design of control surfaces - a very common error in pilot training material where, often, you will see references which, incorrectly, suggest that Va is the speed where the aircraft will always stall before experiencing any structural damage - that may be the case, sometimes, but not always.
So, for the question, presuming you have adequate thrust reserves and are maintaining the speed, you would expect the radius of turn to reduce due to the additional thrust component toward the centre of the turn. This would get you around the turn quicker so the turn rate increases.
I did go through the logic that Bob explained in the Aerodynamics book, but it did not click into my mind. Can someone please explain the logic of the second question in the simplest way please?
You might like to post a scan of just the relevant section of the page in Bob's book so that we are all looking at the same words and then we can discuss.
PS these are the question from CPL Aerodynamics on page 9.21 - Q25/26.
Likewise, if you post a scan of the questions, we are all on the same sheet of music which allows for a better discussion.