#1
My friend thought of "Daylight Falls". Which sounded pretty cool for something that took him literally like 3 seconds to come up with. But I did some searching and I found a very very small time band that has the same name. Should I change our idea? Or keep it? Our music is in the metalcore/punk rock genre. If you can, make some suggestions for one. Thanks

Also we have thought of:
The Almost Ready
Controlled Chaos
Reach the Skyline
"One good thing about music, when it hits you, you feel no pain."- Bob Marley
#2
It's just common courtesy not to take another band's name. My recommendation is to look for something different. You can check the trademark registry (or was it copyright?) to see if the name is registered. If not, then TECHNICALLY it's fair game but you'd still be a bunch of ass-nuggets for using it when you knew there was already a band out there performing under that name.
#3
How am I suppose to get a name trademarked?
"One good thing about music, when it hits you, you feel no pain."- Bob Marley