The white fuzz is likely a fungus of some sort and part of normal decomposition process; the danger from decomposing grass is more likely excess heat (grass decomposes 'hot') than the fungus. The other question mark about grass and leaves is if they have other bugs or residents that eat the worms or simply out-compete them.

That said, you have a very small number of worms - frankly, too few to be sure it will be viable - you'll need several months to get to a decent number. To have a chance, you will need to give them very little food (hardly any, a teaspoon would be plenty, or better, don't feed as I suggest below), and the simplest bedding you can find (my vote would be shredded cardboard or shredded office paper). I'd avoid leaves and grass until you're sure you have a healthy bin. I haven't used coconut fibre, but if it's already in there, just leave it.

If you can find, the safest thing to add as a base would be mostly completed vermicompost (which would have added advantage of probably having some worms or worm cocoons in it), or almost any kind of completed compost (earthy smelling), mixed with a bit of bedding, then cover with more bedding. If you do find, you can (almost) dispense with adding any food at all - worms are very good at 'farming' any remaining scraps of food (or they consume the remains of bacteria, fungi, other residents) and can survive in 'finished' compost for quite a while.

Also: make sure the bin is not too wet. Slightly damp is fine.

Have you read this? It's interesting reading.

[Starting with 2 worms[(https://www.houzz.com/discussions/what-to-do-with-stowaway-worms-dsvw-vd~4972931)

Get some corn meal or masa. If it's corn meal, dig a hole, put a few tablespoons of it in and cover it up. Make sure that the dirt is moist. If it's masa, make a dough ball, dig your hole, drop it in and cover it up. What you are going for here is that if you have any red wigglers nearby in your garden, they will be tempted beyond what they can bear, and come get the corn meal/masa. Just leave it there, and check in a couple of weeks. If any come, collect them up and put them in your bin. Keep doing that until you have a small herd.

What caught my eye but that no one else has commented upon is the mention of using "crumpled up newspaper fliers." If you are referring to the slick inserts with colored ink -- DON'T use that. Plain white newsprint with black (soy-based) ink is ok but as for paper, I prefer brown paper whenever I come across it (like grocery bags - not often since I use canvas bags for grocery shopping - or the brown packing paper that Amazon sends sometimes). I run it through our cross-cut shredder and always keep a bucketful of bits on hand in case I get issues with too much moisture. Toss in a few handsful and mix it in to soak up excess wetness.

In the fall, for years I have saved bags of dry, finely- shredded autumn leaves (mostly maple) to use as bedding. (Be careful not to get freshly-mowed, green grass mixed with leaves as that combo will quickly heat up beyond worms' comfort zone!) But chopped leaves work great, no issues with invaders (well, now & then - see last paragraph), always something there for the herd to eat if I am away awhile or short on kitchen scrap rations. I do have lots of pill bugs/roly polys busily scavenging around on the surface, but they help to break down the bigger stuff for the worms. When I sort out worms from finished compost I pitch scores of the mini-armadillos into a bucket with some leaf litter in the bottom and then pitch the whole shebang out the back door and into the flower bed. Always plenty left behind to re-populate the bins.

Now & then I'll see an orange centipede from outdoors that immediately is given the heave-ho back outdoors. And if a house centipede shows up, it's Death to the Beast. Pretty much always have some mites; not all mites are bad.

And - yes, coconut fiber is harmless as bedding. I'm guessing it'll likely will take ages to really break down, but if so, the compost may be sifted out & the remaining coir tossed back into the new bin.