Yes, you can give probabilities to waking up at 7.30 or marrying a woman you will like. The question is whether you can do so meaningfully.
The logic for allocating probabilities is easy to summarise. You identify all the possible alternatives that could happen. You know that out of all the alternatives one must happen, so collectively the probabilities of the alternatives add up to one. You have considered only the possible alternatives, so their individual probabilities are not zero. So, suppose you have n alternatives. Their combined probabilities add up to one. If you have no rationale for saying that one is more likely than another, you should give them all the same probability, 1/n. If you have some basis for doing so, you might allocate a higher probability to some alternatives than to others, keeping in mind that they must always add to one.
So, consider the question about waking up at 7.30, which I will assume means at any time between 7.30 and 7.31. How might you model the probability of that? You might, for example, say that you usually wake up between 7.00 and 8.00, so there are sixty possible outcomes (ie waking at 7.00, at 7.01, at 7.02 etc). So a very simple model might tell you the probability is one in sixty. Or you might reflect that there have been times- say once a month- when you have woken before seven or after eight. Given that, you might refine your model by saying that you have a one in thirty chance of waking before seven or after eight, and a 29 in 30 chance of waking between seven and eight. So the chance of waking at 7.30 should be adjusted to 1/60 times 29/30. However, that is a tiny adjustment, and its effect is likely to be much less than the error in your original estimate, so why bother making it? You could also refine your estimate by considering the probability that you will die in your sleep and never wake up, but again that would make a negligible difference.
How might you model the probability of marrying a woman you like? That is much harder to pin down. One way is to say that there are three possible outcomes, namely that you marry a woman you like, that you marry a woman you don't like, or you don't marry a woman at all. You might simply say the three options are equally likely, so there is a one in three chance you will marry a woman you like. Or, you might try to define what you mean by 'a woman you like'. Suppose you define it as mining a woman you like sufficiently well that your marriage does not end in divorce. You might then allocate probabilities in a slightly different way. You might look at the national average figures for men getting married to women, and find that x percent of them do. You might look at national divorce rates and find that y percent of marriages between men and women end in divorce. On that basis, the chances of you marrying a woman you like would be x/100 times y/100.
You should appreciate two key points from the examples above. Firstly that it is possible to allocate probabilities, and secondly that there are different ways to do so, each of which might give a different result, so they are simply models or indicatives guides to whether one thing is more likely to happen than another.
A more subtle point is that the meaning of the probability is the set of assumptions you have made in calculating it. What does it mean to say that you have a one in sixty chance of waking at 7.30? It means that you have assumed there are sixty possible times at which you might wake and they are all equally probable. What does it mean to say you have a 1 in 3 probability of marrying a woman you like? It means you have assumed there are three possible outcomes and they are equally possible. What does it mean to say you have an 11 percent chance of living until you are 90? It means that you have assumed your chances are based on national figures for death rates etc etc. It might be that everyone is pre-ordained to die on a specific date, and that you are going to die tomorrow, so the probability of you living to 90 is zero. But you don't know that, so you can't take that into account. All you can do is ask what is the chance that I am pre-ordained to die after I am 90, and based on national figures it is 11%.
You ask a lot of questions about probabilities, and a common denominator to many of them is that you seem to be looking for a more absolute and meaningful way of allocating and interpreting probabilities. There isn't one. All you can do is make educated guesses. All the maths tells you is that the probabilities of all the possible outcomes must add to one- how the probabilities are allocated between the alternatives is a matter of necessarily imperfect judgement because you don't have all of the relevant information.