There is no perfect measurement tool in psychology. This is one paradox in the study of psychology, that we want to understand human behavior in a whole, yet we isolate one factor each and quantify it, reducing man's meaning into numbers and scores. Whether or not the test is usable, or how close it is to the "truth", as in how accurate that tool in describing the factor it seeks to explain (in this case intellectual capacity), depends on its psychometric properties, the value of validity and the reliability of that tool. This method of calibrating how valid or reliable one measurement tool is painstaking to say the least. You want to have a large number of samples, not to mention you have to cluster the age units, not to mention it has to be free from cultural bias, and a lot of other factor. This is why we should take cautions whenever we take a test (especially online tests in the internet) and see our results. We need to know whether the test is valid and reliable, therefore describe acurately our intellectual capacity.
I'll take one IQ test, the IST (Intelligenz Struktur Test) by Amthauer as an example. One of the reasons why the tests must be timed, concerns with standardization of its scores. If it is not timed, the tool cannot differentiate between someone with adequate intellectual capacity, and the one with less intellectual capacity. Because IQ tests mainly measure
general intellectual capacity, it has to be independent of factors such as general knowledge, or common math problems, for the reason that that kind of abilities are not general or raw intellectual capacities, but rather something that is learned and therefore affected by many other factors (i.e. the time spent studying, interests, motivation, etc.). That is why the content of the tests are usually simple number puzzles, matching words, pattern recognition, spacial recognition, etc. They are not the results of learning and can be done without any need of studying one particular subject or at least the most basic of abilities (i.e. language). The amount of time is standardized after a lot of amount of trials, and set as the time the average person can do most of the item of the test. If it is not timed, two person, one is shall we say smart, and another less smart, will be able to finish the test and even with the same score. But we cannot say which one has the better IQ if we only examine the result of the test, because the smart one finish it in, say, 5 minutes, but the less smart one finish it albeit correctly in 25. Intellectual capacity also concerns about the speed of the cognitive process, yes. It is correlated with the "path" one takes in his mental process.
I can't really describe the reason why abstract thinking is the most advanced type of thinking. Try the work of Jean Piaget, that explains our development of cognitive abilities.
Usually if we are talking about IQ tests, they usually measure what we call the G factor (no, not G-spots

). It more or less measures the general cognitive abilities or the intellectual potential that someone has. Mind you, that recent studies show that the correlation between performance and IQ scores has low correlation coefficient. Meaning that how you perform your tasks, succeed in your life or in your job does not depend entirely on how high you score the IQ test. IQ only contributes to roughly 30-40 percent to one's performance.