Don't get your finger in there - definitely cut that off. Seen some local idiots leaving the lid open when cutting - you should also wear some eye protection and don't watch the cutting flame too closely - bounce off the cutting bed does not do your eyes much good. You must have a blower fitted on the cutting head as the fire risk is quite high - in the time taken to answer a doorbell a laser here caught fire and burnt out . The charcoal in the extraction unit can actually catch fire and a thick layer of dust is very dangerous. We clean ours out at 6 month intervals and change the internal flexible ducting. (it has adjustable bed height)
As to the cutting of styrene - one thing to remember when cutting is that the laser cut has a definite width so for small / thin components we have found adjusting the size by .25mm either side leaves you at the width you wanted in the first place. (Found that out the hard way when cutting the parts for a Loyal Moderator). That works on our particular laser but will likely be different on others. Wife has run a Laser since 1993 and I have been using one for the last 10years commercially - great deal more pleasurable than accounting !
The faster the better cutwise, and leaving the styrene to cool between passes is a good idea.