Well it is always a good idea to proceed carefully. Also, this is a good type of question for the hanging forum. That way you will be more likely to hear from Bib as well. Hopefully he will chime in here if he sees this question here as well.
First, move to 20- minute sets, which will help you with your time restraints. Then yes add another set if you can keep hanging. As for hanging days in a row I don’t see a problem. I used to hang day after day for 6 days with no problem. I think you should take at least one day off though. I was not concentrating on fatiguing it properly though. If you are going for the fatigued feeling, and finally get this down, then you will probably have to stop sooner, or at least change to another angle. No it will not hurt you to keep hanging until you get fatigued. That is the goal.
As for the weight, just try and add small amounts. Maybe one pound or so and see how it goes. If it is too much then you can easily take it off. Walmart has one pound dumbbells or you can use a water jug and then add smaller increments. A gallon weighs about 8.3 pounds so just divide it up. You also don’t lower the weight just because sets are proceeding unless you have too.
Don’t be too concerned with the amount of weight. Some days you can hang heavy and other days you can’t. Just develop the ability to determine what is the correct amount for that particular hang (as much as you can without hurting in a painful way). You have to know the difference between a good soreness and bad pain.
I don’t know about lying down, I never did that. Perhaps you mean hanging between the cheeks, which is reclining. Start by getting a chair and propping it up with pillows so you can sit on the edge and let the weight hang strait down. Then after you get the hang of that you can elevate your feet more and more until the weight is hanging between your butt cheeks. However, work up to that and you must lower the weight when you finally try that, because it is more intense. Additionally, you will fatigue much quicker that way too. So,
Move up in weight slowly and cautiously.
Move to 20-minute sets.
Do more sets if you can.
Hang sitting rather than standing.
Dance