No worries. SS is a great program. The great thing about SS is you get a ton of practice on the core lifts which will help you a lot down the road. Most people don't like to hear this but body recomposition goals should be looked at as a lifetime journey. Once you have that perspective it frees you from making short term decisions. If you look at most people in the gym they often never seem to change.
Anyway going back to SS, rookie lifters CAN actually improve strength while losing fat. In fact its quite common. This is because you are still learning the lift, and over time you will get better at it, more mechanically efficient. As far as stalling dont worry about it. Just make sure you have a very conservative start point with SS which will allow you to progress over a long period. A lot of people make the mistake of setting the start point too high and burning out a month later. Ideally you want to be hitting your max efforts with SS about 2.5 to 3 months in. Once you do stall, just deload 20% and start again.
Ok back to HIIT, as a weight loss tool there is almost nothing better. When people are looking for MAXIMUM fat loss in a short time I recommend 3X a week. Again this is dependent on individual goals and recovery, age and athletic ability come into this as well. For your average person 2X is the sweet spot. Start with 2-3 sets of sprints and every week add 1 more set until eventually you can do 6 sets in one session. Rest time between sets is highly dependent on individuals, good rule of thumb is wait until your rate has normalized. That can be anywhere from 2-8 min. Remember sprinting is a very challenging exercise, don't go in 100% until your body has had time to adapt. Generally people can handle 60-80% intensity when starting out. Each week aim to up the intensity slightly. For example week 1 you may only do 2 sprints at 60% intensity. Week 2, 2 sprints at 60 and a 3rd at 80%. Week 3, 1 sprint at 60, then 80, then 90%. Also spend at least 10 min warming up with a light jog, incorporate some knee high jogs and kickbacks.
How you schedule your HIIT is up to you, you can do them at the end of your strength sessions, but you would probably find it easier to put them on different days. This is completely personal preference. Putting HIIT and Strength on the same day means you will have more complete rest days throughout the week. Putting them on different days means less total rest days but more recovery between individual sessions.
I hear you on the calorie counters, and counting calories in general. Thats why I like to suggest people try a 16/8 IF eating schedule. Aside from the fat burning effects of being in a fasted state, in practice skipping breakfast usually cuts the perfect amount of calories for most people to enable them to lose weight. Also doing HIIT while fasted torches fat like nothing else.
If you're not into IF it doesn't matter, it just means you will need to track your calories a bit more carefully in the beginning.