If by “seeds” you mean the bulbils at the top of the stem (that sort of look like mini bulbs) and often referred to as seeds, then yes, you can plant them in fall or spring. If you plant in spring, they will need to have a cold treatment first (place in a breathable bag in the fridge for a few weeks).

If you mean true seeds, you can save the true seeds, but they may not produce plants that are like the parent; the cloves or bulbils are what will be true to type. Not all garlic produces seeds, and those that do produce flowers, may not produce viable seed. If your seed heads are developing, but not mature, then you’ll need to sacrifice harvesting the bulb to let the seed head mature for seeds (which are harvested around October or so), or you can sever the seed stalk (scape) at the base of the plant and place it in water in a sunny location in the hope that it may still mature. It’s best to remove the bulbils early on from the scape (both bulbils and flowers will form at the top of the flower scape) to encourage better seed development from the flowers. The harvested seeds need a cold treatment before they are sown; you can place them in the refrigerator for a month or so over winter. When you sow the seeds in spring, it is likely that the germination rate will be very low for that first generation; successive generations improve. Also, that first round tends to produce problem plants, such as weaker or misshapen, but there’s also the possibility of some with desirable characteristics that you can go on to save further seed or cloves. Garlic is fussy, and has evolved so that it reproduces by cloves or bulbils more often than by seed, so propagating it this way may be a challenge, but could also be a fun experiment! Good luck!

It depends. If the cloves are soft and dried out, of course, they are of no value. Often garlic heads “sprout” or send up greens. Some say that the individual cloves in the head can be planted. Depending on the cloves’ condition, you might have success—but plant a few from this year’s harvest (or buy a couple of heads at a farmer’s market) to know that you will have  crop next year.

It all sounds ambitious and delicious, Reg! Thank you for sharing so many ideas.

Hardneck types of garlic usually produce a flower stalk that will produce small bulblets. These are called “topsetting” garlic varieties.  You can still eat these small bulbs! 

Your first instinct is probably the wisest: You aren’t supposed to plant store bought—better to say, actually, that it often has been treated so as not to grow. You know how sometimes an onion, if left sitting around will send up greens? These are edible. Well, even store-bought garlic does the same thing if you wait long enough, and this is what it sounds like yours did. Transplanting will do nothing but weaken it; it would have to start (whatever it’s doing) all over again. Put it outdoors, if you like. But consider it purely as an experiment. In the fall, get a locally grown fresh garlic head at a farmer’s market and plant its cloves in a pot or in the soil. Just give it some winter and it should be ready to harvest in summer. For details, see above.

Scapes are a good sign. Cut them off to use in cooking (or just discard; the point is, if you leave the scape on, it will use the energy that would have gone into the head). Wait until the greens/foliage dies back then uproot it to see if the clove you planted produced a head.

For edible garlic (not the ornamental type), some gardeners like to trim off the scapes for eating just as they finish curling in their first loop, before the flower bud develops and opens. This way, the plant focuses on bulb growth rather than using that energy for producing flowers and seeds. But other gardeners prefer to let their garlic flower. Since yours are blooming, the scapes are likely too tough now for eating; you can remove the flower scape (not leaves) now, or just leave them be. As to harvesting the bulbs, you can dig them up when the lower 3 to 5 leaves are turning brown–the upper ones will still be green. Don’t wait until all leaves are brown. If you aren’t sure about timing, gently dig up a bulb to check on its size. Hope this helps!

Although it’s best to plant in fall, sometimes the bulbs do sprout in storage over winter. Plant these in spring as soon as the ground can be worked. The bulbs may not be as large, and they may not develop cloves, but they can still be tasty.

Goodness! If your garlic is behaving like the wild garlic weed, then the advice for controlling is likely … just what you have been doing. Hand pulling (preferably after a rain, so the soil is soft, and you can better pull up all of the plant without leaving the bulbs) and digging with a trowel or shovel, especially in fall/winter/early spring before new bulbs form in spring. Fortunately, they are shallow-rooted, but you must make sure to dig up all the bulbs. Do not let the plants form scapes. If the plants are in the lawn, keep up with mowing, which may eventually weaken the plants and will prevent scapes from developing.