So ideally you would work with the support of your health care provider (HCP) to feel this out, especially as you have other health conditions that bear watching!
The basic way it works is that your "slow" insulin is meant to take care of what are called your "background needs" (hence we often speak of a background insulin). Even if you didn't eat a bite all day, your blood glucose readings (BGs) would still fluctuate as your body goes about the basic business of being alive; background insulin is meant to help keep those fluctuations "tamped down" if you will so that your BG doesn't go too high. In someone without diabetes, the pancreas is normally constantly secreting a tiny bit of insulin all day long just for that reason; background insulin is our attempt to mimic that through manufactured means.
Meantime your fast insulin is meant to handle...everything else. So that includes correcting high BGs to bring them into range and also when you need extra insulin to help cart away any carbs you just ate.
What this means first of all is that fast insulin can only really do a good job if the background insulin is doing IT'S job properly - if it's at the right dose. So ideally you would work with your HCP and by trial and error to work out a dose that suits your needs - that is, in the absence of food, it doesn't leave you too high sometimes or too low other times. So that's one step.
Another step is to figure out what your insulin:carb ratios are. This is done mainly through trial and error but ideally you would have some support from your HCP - at the least, to be able to call them up and say "I did X last week and got results ABC, I was thinking of doing Y next week and see if that helps, what do you think about that?" Of course in the real world sadly we don't always get this kind of support. Then we have to proceed cautiously, not make changes too drastic or too frequently, to make sure we don't end up seriously ill or having a serious hypo.
The main way this trial and error process works is that you carefully count all the carbs you eat (ideally note them down somewhere so you have a record you can look over later to spot any problem areas) and, using an insulin:carb ratio you think might work, take the amount of insulin that ratio tells you. Then you have to continue to test your BG 2 hours and 4 hours after eating to see what results you get and whether the insulin ratio did the job you wanted it to do. You do this a few different times and see what kind of patterns you see. If your BG is consistently too high after eating, then you know your carb ratio needs to change so that you take a little more insulin per carb than what you were taking before. The trick is to change it in small increments, ideally not more than 5-10% difference at a time.
One very important thing is that people usually have more than one insulin:carb ratio; you may have a different ratio for each quarter of the day (i.e., a different one at each meal). So when you're testing, you have to consider each meal or time period separately and compare dinners to dinners, breakfasts to breakfasts, etc. to see if you need to make changes. Another important thing to keep in mind is that these aren't like some mystery number that is part of your genetic makeup and you just have to deduce it the one time - how much insulin your body needs is connected to things that are constantly changing like your stress levels, what you normally eat, alcohol intake, activity levels, other medications, and so on. So expect that even once you find a "good" ratio it will sometimes need a little "tune up" to keep pace with all of that!
For your sensitivity factor (also called correction factor, because you're "correcting" high BGs), the process is similar - trial and error, based on seeing how much insulin you need to bring a high BG into range. Again you would want to proceed very cautiously here so as not to go too low!
Now since you might be starting over completely from scratch (changing to new insulins and all of that) what you might want to do is call up your HCP and ask them what they think a good starting point is. For T1s we often start with a carb ratio of 1u for every 10g and a correction factor of maybe 3 or 4 (so 1u of insulin lowers your BG by 3-4 points on the meter), and then adjust from there until we find our "personalized settings." In your case it seems like you might have quite a bit of insulin resistance (that is, you need more insulin to do the job); you might need a different starting point so that you don't end up taking not enough insulin, going too high, and feeling poorly. Hence why I suggest calling up your HCP who hopefully can look at your records and make some suggestions for you!