I believe it depends on how long the artist usually takes to do said thing. Like, if they have a reputation for taking a year, expect a year and ect. Or if you know they have a big list of things to do, might take them longer than usual. When in doubt, I'd just suggest noting them. I wouldn't see anything wrong with asking how its going or a wip if they've started if its a comm. If its an art trade, i'm honestly not that sure haven't had that problem before.
It would depend on the complexity and the prearranged timetable, really.
I constantly am commissioning, so I'm probably a decent place to turn when it ccomes to a topic like this. Now... As for the complexity part of the issue... something like a single character sketch shouldn't take more than a day or two unless the artist tells you beforehand they have a large backlog to get through. Even if they have larger commissions to do, a sketch is quick enough they can toss it in between them and get it done quick.
For larger full colour works, a couple of weeks is more than enough is it's full colour/shade. Add time for backgrounds, especially if complex. Multi-character works with 3+ characters +BG? A month to two months at most should be more than enough. Otherwise the artist is likely taking on more work than they should be at one time.
This is all however subject to prearraged conditions. This is something you should be very clear with the artist beforehand. If the work is a gift and you need it for a certain date? Make sure they know. Better to be turned down and have to find another artist than to get it late. And artists have an onus here too. If your conditions are turbulent or you're swamped with work (art or otherwise), please let the commissioner know. If they're willing to accept the added time for their work, then great!
Personally, I've gotten works the day after I've ordered them, and I've gotten them 6 months later (for various reasons). What you should do, if you plan on commissioning fairly regularly? Find artists you like and trust (either through trial and error or by asking friends) and stick with them. Not saying not to expand your circle of trusted commissionees outwards, just try to find artists who seem to be at least reliable with others. I've taken risks in my time and been burned pretty bad. But it's no reason not to commission new artists whose work you like.
And commissioners? For bloody sake! Treat the artists with some respect! Don't be a pest, if you keep on their ass about your work? Guess what? You're going to get a substandard job and an annoyed artist who likely won't work with you again. So don't do it! We're all better off with happy artists. ^^
Depends on how much communication is going on. Like if the artist has sent a note within the first few weeks with an outline of what's going on/when to expect what bit of work, that's fine, but if it's radio silence while they're clearly active or doing personal stuff, then I tend to hear alarm bells.
That said, I once waited over 3 months for an artist to start work on a commission. They kept telling me they were working on it and even showed sketches and would say it would be done within a week, but then would go silent for another month, even when I practically begged them for a timeline or an idea of when it would be completed (it was kind of time sensitive). This person advertised themselves as a professional artist and had a big name CS owner vouching for them/advertising their work. In the end I just did a PayPal chargeback of the money I'd paid up front and was done with it. They never even contacted me to explain or anything.