I've read that you should fertilize tomato seedlings once it starts growing its true leaves. How big do the true leaves need to be in order to start fertilizing? I've added a pic of one of my seedlings.
You have more than one seedling there.
Recommendation that I've heard and used to follow is to start fertilizing once the first truss has set. Unless for some reason you have a poor starting / growing medium.
Feeding seedlings is optional. Some do, many don't. Feeding or not depends on the growing mix you are using and how long before they can go to the garden.
Looks like 3 there. Those 3 need to be separated and two of them repotted. Bury most of the stems too.
Main thing is if you do feed them be sure to use a well diluted and a nutrient balanced mix and keep it to a minimum. Root development, not top growth, is what is important at this stage.
I'm using Kellogg's Potting Soil that has no fertilizer.
Is it alright to separate them at this stage? Or will it shock the seedlings?
It is only going to get harder on them. Right now, with care it should be relatively easy to do. Just carefully dump out the cup into your hand and carefully work the plants out of the soil and apart. Next time try to do it earlier.
But either way 2 of them have to go. If you don't want to risk it then snip off all but one at the soil line.