None of it is complicated, but a few of these are the difference between a product that lasts years and one that stops insulating.
Coolers are dishwasher safe and BPA free, so the routine answer is: put it in. If you are washing by hand, warm water and normal dish soap with a soft cloth is all it needs. The powder coat is hard but it is a coating, so skip anything abrasive. A wire pad or a scouring cream will haze the finish permanently, and once the coat is broken the bare spot will show against the color forever.
Dry the inside properly before storing. Water left sitting in a closed tube does not harm 304 stainless, but it does eventually smell, and the smell is much harder to get out than it was to avoid.
Do not freeze the body and do not heat it. The vacuum gap between the walls is what makes the whole thing work, and thermal shock is the fastest way to compromise the seal that holds that vacuum. A cooler that starts sweating on the outside has lost it, and there is no way to restore it. Chill your drink, not the cooler.
Rinse the cap separately and let it dry fully. Anything sugary that dries in the threads makes the next swap stiff. If a cap has gone stiff, warm water and a minute of soaking fixes it; do not force it, because forcing a dry thread is how threads strip.
Tritan is dishwasher safe on the top rack only. The bottom rack sits closest to the heating element and sustained heat is the one thing that will deform the body over time. Pull the silicone bumper off before washing so water does not sit between the bumper and the body. For spirits that leave a residue, a rinse with warm water straight after emptying is worth more than a hot wash later.
Store everything with the caps off. A sealed container put away slightly damp is the single most common cause of a stale smell, and leaving the cap loose costs nothing.