I only ever add fertilizer after I remove a previous crop and break up the soil a bit, but should I be adding fertilizer to vegetables that take 10 or so weeks to grow, such as zucchini?
The short answer is "fertilize when the plants need it".
For a longer answer, here are some guidelines that I follow:
(I know I sound like a broken record) Get a soil test done. This will tell you what your soil does and does not have. A good test lab will give you advice on what amounts of fertilizer to add. If you use organic growing practices, the lab should be able to provide advice on which fertilizers to use.
Consult a good gardening book for the requirements of particular vegetables. (I like Ed Smith's "The Vegetable Gardener's Bible" because it provides low/medium/high for N/P/K for each vegetable in an info box on each vegetable's reference page.)
Know your pH, and adjust pH so that the soil is the proper acidity for vegetables. (Generally around 6-7; some like it higher or lower -- consult Smith's book or others to see specific recommendations.) Plants can't take up nutrients as effectively when the pH is too far out of the optimal range.
I add copious amounts of composted horse manure (since it is "free"). I haven't had the compost tested, but based on the soil tests that come back after a few years of adding manure, it seems to be high in potassium and phosphorus. Because of this, I don't really fertilize for P/K, just for N. If you have amendments available locally that you can add, till these in either in the fall, or a couple of weeks prior to planting.
Build up your soil organic matter content. This helps to build healthy soil that holds nutrients and water better, and helps to convert nutrients to a form that plants can take up more readily.
Regarding fertilizing mulched plants, you have three options:
In my experience, if you feed the soil appropriately before planting then you won't need any fertilizer while the plants are growing. You mention zucchini -- I've had incredible growth for an entire season when the plants were put into beds with very rich soil (or when they volunteer out of the compost pile). And on the other hand I've had zucchini which I could barely keep alive even with regular top dressing with dried blood and foliar fish fertilizer because the soil was so poor. It's really important to build great soil; if you do this, then you won't have to fertilize the plants at all during the growing season.
Finally (and the main part of my answer): observe the plants. In my experience, if you have a generally healthy soil and you've been adding compost, the primary nutrient you may be lacking is nitrogen. If the leaves are pale / yellow, it may need supplemental nitrogen. When I see this, I use a couple of different tactics: foliar feeding with fish emulsion (I think it is 1-2-0 analysis, don't have the jug handy now), or side dressing with dried blood (something like 12-0-0). For "hungry" plants (e.g. squash, celery, etc), I typically add a scoop of horse manure to the planting holes before transplanting. This summer that was all the celery needed; I didn't need to do any supplemental feeding. But the squash was in a newly built bed which hasn't had the soil built up over several years, and it needed a couple top dressings of compost as well as a couple rounds of foliar feeding -- the leaves would getting pale and the plants weren't thriving like they normally do.
Frequency depends on how "fast" the fertilizer is. If it's slow to break down, you don't need to apply it very often, and it's less likely to burn (from too much nitrogen at one time) - so unless you're trying to grow giant pumpkins or something, slow is better, IMHO. Even with slow fertilizer you can apply it more often than you are. Whether you need to depends on what's in the soil already.
I prefer a "balanced" fertiliser, e.g., 10-10-10 - not something with lots of nitrogen.
I also rely on other soil amendments - composted manure, turned-in winter rye, and my own yard compost, in widely varying amounts. These are applied once a growing season. If I had to choose only one amendment, it would be store-bought composted cow manure. These amendments improve the soil structure, in addition to providing slow-release nutrients, and thus are a lot more beneficial than chemical fertiliser.
Yes, you can apply fertiliser over mulch. Some of the nitrogen will be lost to bacteria breaking down the mulch.
In general, just experiment cautiously and observe carefully how your plants react. If you over-fertilise, you'll see some immediate tell-tale yellowing or wilting.
