^ Sure, plants can be considered alive or dead, and the radishes were still alive when bought from the store, slowly dying but were "alive", and I could have even planted them in the ground if I'd wanted a certain % to survive and go to seed.
I have a shorter term and longer term compost, the longer gets citrus peels, pineapple rinds, banana peels, acorns, tree & shrub twigs and cuttings, etc, anything that takes more than a few months to break down. Shorter term gets non-woody weeds, leaves from the prior vegetable garden, plant based kitchen scraps, coffee grounds, tea leaves, and onion scraps as well.
I compost everything plant based, and don't notice the acidic foods causing excessively low pH, but it may be due to a couple factors, one being the egg shells (eventually, see below) and other materials neutralize acid, and the other being that the majority of water my garden receives comes from tap water which is slightly alkaline, and somewhat hard so those minerals counteract acidity too, and that acidity makes them bioavailable by conversion into a salt, for example fruit, citric acid + eggshell = calcium citrate.
Egg shells on the other hand, get thrown into a coffee can, crushed with a piece of 2x4 when the can gets full, then put into another container. I don't try to make them break down before mixed into the container or garden plot soil, but I mix into the soil months before plants go in.