I don't know if I'd consider the cut I use for stir fries to be a jullienne, as I tend to make 'em a little larger, as I like a little bite left in my vegetables. (I consider julienne to be at most 1/10 of an inch / 2.5mm across ... I cut my carrots for stir fries at maybe 5mm across)
I tend to julienne when adding vegetables to cole slaw-like salads (or even apples and other firm-fleshed fruits).
If you like really crispy fried potatoes, you can julienne the potato before frying to make 'matchstick potatoes'.
Many professional chefs will have a mandoline, and so if they're preparing large amounts of something, they'll use that, rather than a knife. (and you can get longer strips that way ... the full way down a large zucchini or long cucumber, which would be difficult with even a long knife).
Julienne is also just a step before finely diced items, so technically, I'll pass through that phase when cutting up carrots for mirepoix.
... all that being said -- you're probably most likely to encounter the term when dealing with fancier french cooking or "gourmet" type recipes where you're trying to impress a dinner party. "Home" cookbooks are less likely to get into complicated knife tasks.
You can do anything with this knife that you would do with your santoku or Western-style chef's knife. These are real tools, and they are not especially delicate. It is certainly possible to chip the edge or tip (which requires an annoying amount of work to fix), if you drop the knife or, as the manufacturer warns, whack it against bones. This is a consequence of the relatively high hardness of your blade -- not of the fact that it's a gyuto -- but the flip side is that it should retain its edge very nicely for normal work. (A softer steel would end up with a rolled edge or dent rather than a chip.)
I guess that by "chopping" you mean quickly lifting and pushing the blade down through food so that it hits the cutting board. That's perfectly normal usage, and a plastic, wood, or rubber cutting board should not hurt your knife at all. (No glass! Do run it over a steel it often as you use it, though.) The foods you mentioned -- potatoes and fruit pits -- may seem hard, but they are much softer than the edge of your knife.
Best Answer
Although this is partially personal preference, in general you should have the uncut ingredients on the side of your non-cutting hand. This will set up a logical flow of material which keeps you from having to reach over your cutting hand.
If you chop with your right then you'd have the uncut ingredients on your left, as after knife work your chopped ingredients will be on the right of the knife. Everything else comes from this. If you are chopping a lot of ingredients it makes sense to have a few bowls handy to put the chopped ingredients into so you can keep your board clear.
My workflow is based on the assembly line principle - that is do all of one type of task before moving onto another to limit the amount you have to move: before chopping I get bowls for each of the chopped ingredients (stackable stainless steel bowls from a kitchen supply store are great for this as they clean easy and take up little space), and array the bowls to the right of the board. Then I wash all the ingredients, peel them, and prep them at once rather than doing it individually per ingredient and place them to the left of the board, so I have all my ingredients ready to chop. Then I take each type of ingredient and chop them one at a time, saving any messy (tomatoes, cheeses) or possibly contaminating ones (meat, seafood) for last, as I will have to clean the board, my hands, and the knife after possible contaminators to prevent cross-contamination. As the board fills for each ingredient I will transfer the chopped ingredients to the bowls, but I wait until I need the space to continue cutting - if you move the chopped ingredients each time you finish chopping one of them then you waste time moving your arms and body around.
This is the fastest way I have found to get a lot of ingredients processed. If you wash, prep, peel, chop and move each ingredient individually you spend a lot of extra time moving around the kitchen.