On the IQ test: you have one score that gives raw scores, and another that is adjusted for, say, age. Assuming the adjustment makes sense, you can and probably should use the adjusted score.
Here's why: you know that IQ depends crucially on age, that's why you would ideally want to adjust for it. If you only had the raw scores, you could build an adjusted measure by yourself (assuming you have age of the subject). The easiest way to do this would be via interactions. A linear regression like
$$MemRep_i=\beta_0+\beta_1 Age_i+\beta_2 RawIQ_i+\beta_3 Age_i\times RawIQ_i+e_i,$$
accounts for the fact that the influence of IQ on your dependent variable varies with age. For example, an estimate of $\beta_3=.2$ would mean that every increase in the product $Age*RawIQ$ increases your MemRep score by .2 (I don't know if the scaling makes sense, but you get the idea). This is not to be confused with the direct effect of age, which is estimated in $\beta_1$, or the direct effect of RawIQ ($\beta_2$). In the above specification, however, the interaction is constrained to be linear -- this is the simplest way to adjust, but may be very restrictive or simply wrong. I am guessing the adjusted IQ scores you have are more sophisticated and should therefore be used. Using the adjusted score then replaces the RawIQ and interaction above, i.e., you would estimate
$$MemRep_i=\beta_0+\beta_1 Age_i+\beta_2 AdjIQ_i+e_i.$$
Clearly, this is more convenient (and probably more accurate) than building the adjusted score yourself, especially since you mention IQ does not only depend on age, but also schooling etc., for which you would have to add interactions as well. The one exception is if you think these linear interations produce a better adjusted IQ score than what you have.
The question whether you should use raw or adjusted score for your dependent variable is a different story. I would say the choice is mostly driven by your task: you want to predict the MemRep score - the adjusted one or the raw score? In particular, if you do not have access to adjusted scores later, then there is no point in building a model that predicts adjusted scores, and you should stick to the raw scores. As a side remark, if you estimate a model with adjusted MemRep score and do include predictors that have also been used in the adjustment, then you can actually see whether these predictors have predictive power left. If some predictor is significantly different from zero -- say age is positive -- that would mean the adjustment did not sufficiently account for age differences and with higher age of the subject you would predict a higher MemRep score.
Last remark: since you want to predict well, divide your data set randomly into training and validation data set. You estimate the parameters using only the training set, and then predict the MemRep scores for the validation sample. Do this with different speficiations (using raw scores, adjusted scores, with/without interactions etc.). Then just stick to what works best.