The “little plants growing out of the sides of the stalk” are called suckers. Remove them regularly, they will stunt the plant's growth or even kill part of it. Never attempted to plant one, can't say about that.
Same goes for the blooms. Allowing blooms to remain will stunt the growth of the plant, think of petunias going leggy from lack of deadheading. “Top” the plants regularly, do not allow blooms to remain for long. As an ornamental rather than a crop, the blooms can be pretty, from almost white to pink, looking like Nicotania (a relative as the name indicates) or the petunias mentioned, but on a tall stalk with large leaves.
As far as pests, contrary to what the author says about New Zealand, here there are a few, in traditional tobacco growing areas at least. Tobacco worms are ugly, big green things that will sting you. Think of tomato worms. They will damage and eat a surprising amount of tobacco. The old school method of ridding yourself of them is to go down the rows every couple of days wearing work gloves carrying a bucket of kersosene, picking the worms off by hand as you see them and tossing them into the bucket. Be very careful of your choice as far as pesticide if you go that route, remember the leaves will be smoked, entirely different from washing, cooking and eating a vegetable.
The plants like full sun and hot, humid weather, thrive on it. They like rain but they also like dry feet so don't over-water, they'll “drown” which will stunt and possibly kill the plant. Ideally the conditions would be more like a typical southern summer, hot baking sun with a decent drenching from a thunderstorm every couple of days, soil drying out visibly on the surface in between.
Your bedding plants or seedlings, typically these are grown in a bed (window box for the hobbyist) until they have a healthy enough growth and root system to survive transplantation. This will be taller than what you'd see in a flat of tomatoes but this is due to the leaves, it's a useful scale of reference. Planting would depend upon growing season in your location. Certainly get them in by the end of May, you'll want the leaves all pulled and harvested before first frost which ruins what's left.
There are many varieties of tobacco plant. What the author describes is rarely grown by actual large scale tobacco farms anymore, but it's far prettier. Commercial hybrid varieties are now more compact, not so tall with tightly spaced leaves. Go out pulling tobacco for a season with the old variety, and then try it with the hybrid, you'll quickly gain an appreciation for the ease of harvesting the new, aesthetic considerations aside. Brightleaf variety is what is used for cigarettes. Burley is more often associated with cigars, pipe tobacco and so on.
Curing can be achieved in a matter of a month with application of heat in a controlled environment. This is so-called flue curing, done in log barns with a fire and a flue originally, hence the name. Fires had to be tended, it was an all night affair, could be fun if your barns were in reasonable proximity, stews and pig pickings, music and homebrew, it was a backcountry excuse to stay out all night and whoop it up a little. Pretty boring otherwise just tending the fire by your lonesome. This is done now in electric or natural gas fired bulk barns, like truck trailers, the tobacco from these isn't nearly so pretty but it gets it done I guess.
There's a lot more than that but you get the picture. My family came to Maryland in the mid-1600’s as tobacco planters and remained so right up to my dad's generation, then they saw the writing on the wall and got out. My summers from age twelve up to age eighteen were spent working in the tobacco fields of relatives and neighbors.
Speaking of that, wear a longsleeve shirt to pull the tobacco leaves as they start to turn. The nicotine is sticky, it gets in the hair on your arms and is difficult to remove without some sort of solvent. It will also absorb through your skin and can really make the world spin out from under your feet if you're not a smoker. Think motion sickness for a comparison.
Oh well, I'll stop now, lol.
I sprayed mine with bacillus subtitles for the worms. Worked well.