Welcome to Reef Central and the hobby.
You are likely to get different answers to your questions as, there are many ways to be successful in this hobby. The key item is to be patient and take your time. Nothing good happens fast in this hobby.
Caribsea life rock is really just dry rock that has been infused with nitrifying bacteria to help jump start a cycle. In my opinion, this is not really live rock.
I prefer to use a mix of dry rock and real live rock offered by companies such as Tampa Bay Saltwater, KP Aquatics, Gulf Live Rock, Salty Bottom Reef Company and Walt Smith. This rock is actually old coral reef that is mined on land, pressure washed and placed in the ocean for a period of time (usually years) to build up bacterial populations and will usually have various hitchhikers like sponges, macroalgae, corals (if you're lucky), and sometimes shrimp, crabs, urchins, etc. Some vendors here in the US also offer wild collected Australian live rock which looks fantastic but, is very pricy...last time I looked it was $25/pound.
I have never used a roller mat so, I won't comment on those.
Running a skimmer during the cycle or not depends on who you ask. Many do run a skimmer and many do not. Both ways can be equally successful. I personally run a skimmer during the cycle.
I've never used a bacterial products (like the Red Sea kit you reference) to cycle tanks either but, have heard good things from those who do.
Some people say to do water changes during the cycle and other say not to. I prefer to perform water changes during the cycle.
Some people say to leave lights off during the cycle and others run their lights. My preference is to run the lights during the cycle to help maintain the any light needing inverts/corals/macroalgaes on the live rock.
Hope this helps. I'm sure others will chime in. Don't hesitate to ask more questions and we'll do our best to help out.
I've been in the hobby since the 1980s and there are members here who have been much longer than me. So, quite a few of us have seen all the trends, changes, innovations, etc in the hobby over the years.