Your 8" pots will be far too small for mature plants. Consider them as an intermediate step for 'potting on' - meaning transferring seedlings to the next-size-up of pots.

However, they might just do for the chives. Even one little bulblet will eventually propagate itself into a nice little clump, which (in the right growing conditions) will fill an 8" pot in no time flat. They do not 'meld together', as you say, although a heap of seedlings in one pot will give that impression. You can choose between transplanting one bulblet at a time, or transplanting the whole lot into a larger pot. Probably more aesthetically-pleasing to do the bulk move!

In the right conditions, a mature basil can be the height of a child (say, about 10yo), and roughly the same width as its height. You'll have a hard time accommodating that in an 8" pot! When transplanting, select only the healthist-looking seedlings, and discard the rest, then put one seedling per pot. Of course, you don't HAVE to discard the weaklings - they can always go outside in the garden, where they'll probably do better than the ones inside. You're bound to lose a few, of course. Basil is an annual, and you can expect it to die come next cold season. Basil starts flowering from a very young age. You can try to remove the flowers to encourage more leaf growth, but when you discover a way to prevent it flowering more and more, please let me know!

You can start re-potting your basil right now - they are a fast-growing, greedy plant and need space, full sunlight and heat to grow (that does NOT mean the filtered sunlight of a glass window, nor the reflected heat from glass which can easily burn the leaves). Don't start pinching back until you have, say, 10 pairs of leaves, and then just remove the top pair or two.

Parsley doesn't like being transplanted, but you'll have to give it a go, as the current pots are miles too small. Don't pinch back parsley - let it do its own thing. Next time, put 2-3 seeds per pot (in which the mature plant will fit - ie 'sow in situ'), then discard the weaker two. Still, give it a go, remembering that parsley has a long tap-root that is easily damaged, and doesn't like being fiddled with. Parsley grows from the centre (think of an erupting volcano), so harvest the bottom, outside leaves, and leave the centre baby leaves to grow to replace the oldies. Remember, parsley is a biennial. In its second year the leaves become coarser in flavour, and the plant will go to seed. Let it happen. Treat Italian parsley in the same way, but remember that it will grow to a considerable (and, to a newbie, substantial) size that might just squeeze into your oven without too much scrunching when mature.

Chives and parsley can both do well in partial sun, but basil needs full sun, and lots of it. All your plants will be much happier outside than in, and you can expect them not to grow to optimum size or quality in pots.

When dividing seedlings, tap the starter-pot firmly but gently around the sides and bottom, and tip out the contents onto a table, laying the pot-shape on its side. Then carefully break away the surrounding potting mix to expose the roots of the plant. Carefully remove each seedling, being careful not to damage the roots - if they are pot-pound, you might have to do a bit of 'teasing' to disentangle them. Have ready-prepared another pot, with fresh potting mix, use a dibble-stick or your finger to create a hole deep enough to accommodate the entire root system, insert the seedling, then using your fingers only, gently tamp in the soil around it, making sure NOT to bury the plant any deeper than it originally was. (In other words, don't bury the seedling any deeper than 'the dirty line'.) Water in carefully, and Robert's the other son of your grandfather.

In future, I suggest that you learn about your plants BEFORE you start them - mature size, growing conditions etc. But yes, you've experienced the delightful thrill of seeing something small and brown actually turn into a plant - and there's no better reward than that.