Question:
2) Where is the 0.05 and -0.05 in the yellow highlighted portion from? The only 0.05 I see so far is the monthly active risk, but that is not linked to returns, right?

Can someone explain this statement to me? “If active risk is limited to 5.20%, the deviation from the benchmark weights of 65% and 35% is limited to (5.20% / 17.32%) = 30%.” I do not understand the concept behind this.

In the answer to 2, you have a formula
annualized active return = IC \times \sqrt{\textrm{BR}}\times \sigma_{A}
where \sigma_{A} is the annualized active risk,
so yes, active risk is linked to active returns.

The expression you have highlighted in yellow
(0.60)(0.50)+(0.40)(-0.50)=(0.60-0.40)(0.50)=IC \times\sigma_{C}

3: The active risk if the deviation from the benchmark is 100% is 17.32%
I assume that 100% deviation from the benchmark means either
staples 165(=65+100) and discretionary -65(=35-100) or
staples -35(=65-100) and discretionary 135(=35+100)

The active risk is proportional to the deviation from the benchmark:
If the deviation from the benchmark is x\% then the active risk will be (x/100)\times 17.32\%

You need to find the value of x such that (x/100)\times 17.32\% =5.32\% ,
so x=100\times 5.2/17.32=30\%

I think you need the help of an expert like S2000magician or Mikey here

As you say, the formula in the answer they give to q2
annualized active return = IC \times \sqrt{\textrm{BR}}\times \sigma_{A}
should be
annualized active return = TC \times IC \times \sqrt{\textrm{BR}}\times \sigma_{A}
where TC is the Transfer Coefficient
However, when there are no constraints, the Transfer Coefficient TC =1, so for 2., the formula
reduces to the formula they gave.

For 3., there is a constraint (the active risk can’t exceed 5.32%), so the transfer coefficient will be <1.
I’ve got a suspicion that TC =0.3 (from the 30%) for 3. Hopefully one of the experts can either confirm this or set us straight,