is a nice short reference for which silicones are CG friendly.
Pure Clean conditioner, and Biolage Firm Hold Gelee are both CG friendly. The O'pro leave in is too (no sulfates or silicones), but it has a drying alcohol (SD aLCOHOL 40-a) as the 2nd ingredient which can leave your hair dry /frizzy. I would find a different leave in that's free of drying alcohols, but that's personal preference. If you choose to continue using it, just watch your hair for dryness /frizziness.
Any silicone that begins with PEG or PPG is water soluble and can be removed with conditioner washing, so your Round Trip is also CG friendly. Magnesium Sulfate is curl enhancing but can be drying too (it's a salt), so just watch how your hair responds over time.
The short answer on Super Skinny serum is that it is not CG friendly. The longer answer is that dimethiconol, trimethylsioxyamodimethicone, and amodimethicone are all not water soluble, so they need a silicone free low poo (sulfate free shampoo) containing cocamidopropyl betaine or cocobetaine to remove. A sulfate shampoo will remove them too, it's just not as gentle as a low poo.
isn't water soluble, but it's a special class that evaporates off during the drying process, so it can be cowashed away too.
The amodimethicone and trimethylsioxyamodimethicone are another special class of silicones that target damaged areas. These silicones and others in the same "class" are not water soluble and do require a silicone free low poo or sulfate poo to remove. However, once one layer is deposited onto the hair shaft, it repels any further deposits, so these silicones tend to resist building up.
You do not need to purchase a separate clarifying shampoo. You don't necessarily have to clarify monthly either. Most curlies clarify only on an as-needed basis. For some, that's weekly, for others, monthly, yearly, or even less often. It depends on the individual head of hair and local water quality.
Many curlies choose to use a silicone free low poo as needed for clarifying silicones or other product buildup. Any sulfate free shampoo with cocamidopropyl betaine or cocobetaine will remove any silicones on the hair. For some with hard water, they might need to occasionally clarify with a chelating shampoo to remove mineral buildup from the area water.