From your description of how it died (center out with browning leaves) it does sound like root-rot. Did you use a different type of soil than previously? The soil could have more of a clay consistency that held water better than the previous. Or, it could have been a weaker plant that was more susceptible to start with. I baby my potted rosemary like crazy, but the larger "tree" that I purchased still semi-died. All the new growth since I got it is fine, but the original is gone. It's an interesting experiment.

If you live in a hot/warm climate, your basil and your rosemary will grow to quite big plants. The basil, being an annual (which means it will die come winter) will be the fastest to grow - probably at a rate of knots. It will definitely be happiest outside, in full sun. You can use the leaves at any time, but don't trim off more than one-third of the entire plant at any one time, and allow it to grow back before harvesting again. Trim it, it grows, and will become a nice, full (ie not leggy or too woody) shrub. Yeah, get rid of the dead leaves - they're unsightly, and quite useless except as mulch. You can take cuttings of basil at almost anytime during the growing season. Forget the water thing - cut a strong stem on an angle, dip the end into pure honey, chop off the tender top leaves, stick into some potting mix, and Robert's son of your grandfather. Rosemary is a very large shrub when it's grown up. It also prefers to be outside in the full sun with plenty of room to spread. It also can be trimmed back regularly to keep it bushy and unwoody, and it can also be propagated from cuttings, preferably heel cuttings from the previous year's growth. Just look for a satisfactory sprig, then peel it off, tidy any stringy bits, dip the end (which looks like the heel of a shoe) into honey, stick into some potting mix, and Robert's......It's a slow-grower, especially in its first year, but since it can live for about 30 years or so, that's OK. As for coriander (which you call cilantro), that's another kettle of fish altogether. It's a very short-lived annual. In hot climates, its entire life-span can be as short as 2 weeks - from seed to seed - so you'll need to get more plants until you establish a nice little patch which will soon look after itself. Allow your first plant to go to seed, and then watch the babies grow. Soon you'll have plants in all stages of growth. If you want the leaves, collect them before they start to turn lacy - that is a sure sign that the plant is about to go to seed, and there's nothing you can do to stop it doing its Thing. In hot weather, you'll need to offer it some protection from the worst of the heat - which hastens the 'bolting to seed' process. Again, it's happiest outside, but in a hot climate, give it dappled sunlight to slow things down a bit. Since this plant self-seeds readily, and grows so quickly, there's no need to propagate by cuttings, though it can be done - same method as with basil. Easier to buy a small seedling every couple of weeks until your patch is up and going. These plants CAN be grown inside for a while, if you're quite happy with severely stunted plants which are susceptible to bugs and diseases, dust and grease and rapidly-fluctuating temperatures (such as in a kitchen) All need excellent drainage, and that can rarely be provided indoors. Also, being next to hot glass, they'll burn easily (touch the glass on a hot afternoon and see if you'd like to sit next to it!) and they'll never be happy plants. Nature didn't invent houses, so didn't invent plants to be grown in them. Plants are very like humans in a lot of ways - we all like plenty of fresh air, room to spread out and grow (we don't want to bind our feet to keep them from growing - well, plants don't like their roots being confined either), enough water to sustain us but not drown us or rot our feet, sunlight, and freedom to do our own thing (but being protected when we're babies). Make sense to you?

A Misco or Misco-type pot is a plastic, self-watering pot often used for semi-hydro (s/h) growing with orchids. Misco is a brand name, hence, there are others out there without the Misco name. The pot is basically composed of two parts, the upper part with holes which inserts into a lower section which serves as the reservoir. The reservoir is filled from an opening on the outside of the pot. Misco and Misco-type pots are readily available at most garden shops and discount stores. Image by: Donna Phillips Misco or Misco-type pot

Rosemary is finicky in containers. If you dont have a frost danger, get it outside where it can get lots of light and some natural predators and wind to mitigate the spider mites. Check your drainage and consider reporting into a citrus/cactus type potting mix because rosemary will get root rot in consistently wet, soggy, or compacted medium. Let the soil dry out between waterings. Consider clipping the worst of the dead stuff back and see if you can get new grow th further down and keep the shape from getting too leggy.