I have planted Parsley(one in the green pot) and some flowering plants in small pots indoors with holes at the bottom for drainage. I've seen small white pebbles recently which when I googled seem like calcium which usually deposits when the water is not draining properly. I water them with a spray bottle and try to water them once every two days or whenever the soil feels dry. I have since then seen a couple of videos but they suggest watering indoor plants under the sink. I'm a little scared of doing this since these are very small in size and I don't want to flood the pot. P.S.: Any suggestions on what's the right technique of watering small plants will be helpful as I'm a novice in gardening. Also, what should I do with the calcium deposits, should I remove them or let it remain in the pots. Attaching a few pics.
The white pebbles are probably perlite, this is often mixed with container soil for better drainage. Nothing to worry about, it is not Calcium deposited or anything like that.
Spraying would be fine, just keep them watering like you do.
However, your seedlings seem a bit leggy (long and thin). This is caused when the seedlings do not get enough light. My advice is to put them in direct sunlight. Some seedlings are so long already that they can't support their own weight (in the orange terracotta container and in the pink one).
The watering instructions you've been reading are not for seedlings, they are for much bigger plants. Your seedlings will not tolerate direct sunlight, but they would do better with brighter daylight.
As they get bigger, with a second or true set of leaves, they will need to be pricked out into individual pots, not left altogether in one large pot, or they will not grow on properly. The only exception to this is if you are growing what's known as a 'cut and come again' crop, which usually consists of leafy plants such as lettuce which you intend to eat when they are leafy, but still small.
In the meantime, continue watering as you are currently doing.