Also, how do you feed with compost after they've been planted? I've
mixed compost in the soil when i plant them, but can i just sprinkle
compost near the base and they'll absorb it?

For annuals like tomatoes, mixing a suitable amount of compost into
the soil at the start of each season should be enough. It is
naturally slow-release, especially if you avoid washing out nutrients
by excessive watering.

For perennials like turf grass, flowers, etc, or if you prefer not to
till, yes you can spread compost on the soil and let the rain and
earthworms distribute nutrients. One common version of this is to
mulch with an organic mulch like wood chips, leaves, coffee grounds,
etc, and let it eventually decompose. You can also fertilize with
liquid organic fertilizers like compost tea, compost leachate, or fish
emulsion.