Being "reputable" is something separate from being "good" or "experienced." You can be reputable as soon as you start offering your services by being honest (and realistic) about your capabilities and by delivering exactly what you promise to deliver from Day One. You become good at this and experienced by doing a lot of it over a relatively long time, pretty much the same as most other professions. The anonymity component is probably similar to many other online services and it typically goes both ways with many customers preferring to identify themselves only by an email address at first. Once you've done a couple of transactions with someone, both parties generally drop any initial reservations about identity disclosure. The only results you can "guarantee" are that you will fulfill the specs provided and that the writing will be at the quality level that you promised and that customers will feel that they got their money's worth at the time they receive and review the product you provide.
I've never had much difficulty cranking out a B or a B+ essay throughout school (at the undergrad & grad level) - are prospective students looking for As or are they generally content with decent passing grades?
It depends on the customer. Many are A students who expect your work to be the same general quality as theirs; others expressly request it not to be more advanced than their writing samples that they provide. Sometimes, you get parents placing orders and requesting that you don't write beyond the level of a high-school student, 8th Grader, or even (one or twice in my career) the level of a 5th or 6th Grade student. Customers who are ESL often request simple language and sentences, but I've also had ESL clients expressly request language as "complex" or as "sophisticated" as possible.
When I started doing this, it was strictly a supplemental income and I could not even imagine writing enough or as fast as would be necessary to provide a comparable income to a decent regular job. It's not something you'll ever become wealthy doing, but if you like the independence of it, you can definitely make it work. Nowadays, I gross more than my last pay grade as a Senior Writer/Editor for the U.S. federal government and I could never even consider going back to a regular 9 to 5 again (more like 7 to 3, by choice, to beat the rush hour) just to earn the same money or even slightly more. I'd have to make substantially more than what I earn doing this just to consider another office job; but I'd definitely go back to teaching hockey or bouncing at a strip club for somewhat less, if a steady, long-term offer like that came along =)
To writers with stable freelance jobs: how long did it take you to build up a steady supply of work? Was it all word-of-mouth?
For the first few years, most of my income was from essay companies and I had only a handful of freelance clients, most of whom were either acquaintances or referrals from acquaintances. More recently, almost all of my work is freelance and essay-company work is less than 1/10th of my income. I wouldn't necessarily say it's "word of mouth" either: it's more like you (very) gradually get to where you have about a dozen or more regular repeat customers; then, it's just a matter of continually getting enough new clients to replace the ones who graduate. Even if you're very good at this and very experienced, it would still take some time to start all over again to go from having no clients to having enough clients to sustain yourself doing this for a living exclusively.
You definitely get better with practice: most new writers specialize in longer deadlines and work much the way they did as students, laboring for several days over every 10-pg paper. By the time you've written 1,000+ papers, you start specializing is rush work that pays more and you typically bang out a 10-pg paper of ordinary undergraduate-level of difficulty in a few hours, maybe with a meal or TV break in the middle. You no longer need multiple "drafts" anymore, either, because the first thing you write comes out pretty polished and rarely needs more than a spellcheck and one proofread.
There's no way to use any kind of "syntax database" or a sentence template, because if you're a good writer, that would take more effort and time than just free-writing. You might have a template of standard headings and font settings, but that's about it. Generally, people who are not naturally good writers tend to assume that anything other than writing from scratch is helpful and several non-writer acquaintances have asked me the same question and then looked at me like I was BSing them when I told them that you can't write academic papers (or much of anything, really) the way you fill in "Mad Libs" party games. For experienced writers, free-writing is the fastest process there is. About the only thing we do along those lines is keep a database of good reference material on various topics so we don't have to re-type every book or journal article that's useful for more than one project, especially those that you actually have in hard copies in your library at home.
Do you ever offer any sort of proof of qualifications to potential buyers, or is that futile because these days just about anything can be photoshopped?
I believe it's futile but for an entirely different reason: The only objective "qualifications" you can provide are that you have a particular degree, but having a degree in most academic fields has little to do with how well you write, especially if you're writing in many more subject areas than your formal educational background as you must be able to do if you hope to make a decent living at this. About all you can do in that respect is prove that you don't just grab at any work dangled by declining projects that you can't take with confidence and by providing good work on the first small test project from any new client.