If the grass is attached to its roots and dirt, they can usually bite off pieces that are safe to swallow.
If you cut the grass (with scissors or a lawn mower) and give the cut pieces to chickens of any age, then they swallow whole pieces, of whatever length you cut it at-- and sometimes that is long enough to make tangles in their crop and get stuck there, not able to go further down but blocking any other food from going down too. If that does happen, and you don't fix it somehow, the bird will eventually starve to death.
Whatever size chunk you have conveniently available. If it rains and the sod chunks get wet, don't put a soggy muddy mess into the brooder. A bit damp can be fine if it there is still plenty of dry space in the brooder.
Not a big deal, unless those bits get more stuck to them, and it collects into a big mess that does block the vent. Sometimes it is worth picking off the bits (especially if you see that more is sticking to them), other times you can leave them alone and they never cause any trouble.
Second heat emitter: no. If they already have enough warmth, more will cause trouble. Too much heat is one of the major risk factors for pasty butt, among other things.
Roosting bar: you can put one in if you want. Young chicks like to cuddle together on the floor to sleep. They will switch to roosting as some age (varies widely from one batch of chicks to another: anywhere from 2 weeks to 4 months, and possibly earlier or later than that.)
They do stay cleaner if they have clean bedding where they sleep. A flat surface like paper towels will get "dirty" faster than something like shavings that they can mix the droppings into. I'm not saying you need to change anything about the bedding, just mentioning that different beddings do behave differently.
