How long a carto lasts depends heavily on how you use it. Puffs don't come in standard sizes
Basically, you just have to get a feel for it. Vapor production will drop off gradually. When the taste changes slightly, you're almost at the end. If it starts tasting singed/burnt, you've gone too far. You'll definitely notice if you get to that point, there's no missing it. This will happen at least a few times, till you get a feel for it. If you don't plan on refilling the cartos, that's really not a big deal. If you do want to buy liquid and refill them, avoid getting to that point if possible.
If it helps, I used to smoke about a pack a day, maybe a little less. When I started vaping, a carto would last me about 2/3rds of a day. But that's a very rough guideline, at best.
If the light flashes, that's the battery running out of power. Has nothing to do with the carto.
Lithium-Ion batteries do not care about being fully charged and discharged on first use. That sort of advice is a relic from the olden days, when NiCad batteries were the norm. You can charge and use Li-Ions however you like. You can even be charging, take it off the charger, take a few puffs, put it back on the charger. In fact, they prefer being in a perpetual state of half-charge. Never full, never empty. Doesn't make too much of a difference either though. Just use them however is most convenient. Practically all batteries you will ever encounter these days are Li-Ion.
Do make sure to buy more cartos long before you run out. Might as well get on that right now. Nothing is worse than running out when you've just started and being forced to go back to the tarsticks while you wait for the mailman. If you stick to vaping exclusively for even a couple of days or so, real cigarettes will start smelling and tasting nasty. Really nasty.
Getting eLiquid and refilling is much more economical. And opens up a huge variety of flavors. Cleaning, refilling and maintaining cartos can be a hassle though. But tinkering with them can also be fun and rewarding. It's up to you whether you want to spend the time and enjoy the benefits, or just want to buy and toss pre-filled cartos for convenience.