Most summers you can put them outside once the weather warms up - in fact my 25 pots full were outside (in the warmest sunniest spot we had) most of this summer until I turned what had not been used in cooking into pesto. They need good air circulation and they also like their feet to be kept relatively dry - I suspect yours have been too damp, given that the fungus gnats seem to have invaded the pots.
Don't worry about spraying fungus gnats, just keep the compost a bit drier.
I sow sweet basil seed thinly in a tray in early spring and pot on into little plastic pots when they have two proper leaves - they grow very slowly until the weather warms up when they grow like crazy and need potting on again - I put three plants in a 6" diameter pot and they stay there. Pick leaves from the sides, don't pick out the tip.