You'll find that, sometimes, people take a small bunch or single flower to a church/cemetery funeral as people may throw a flower on top of the coffin once it's in the ground.
But with a cremation, the coffin 'disappears' either down into the ground or through a gap in the wall by hydraulics. So there isn't an opportunity to put anything on the coffin really.
Any flowers brought in with the coffin will be removed by the funeral directors before the coffin is moved away for the cremation 'disappearance' itself. Those flowers will be from family and friends who have ordered wreaths etc and had them delivered to the funeral directors or to the home depending on the wishes of the family.
The flowers, if there are any, are usually taken out of the service room before everyone leaves in a cremation and placed outside nearby so, as you come out, you may find people wander over to have a look at them. It's often a nice ice breaker as you can comment on the lovely wreath or beautiful peonies or whatever - and that open the conversation to how did you know x?
Don't feel obliged to go to the wake if you feel you can't. Just try to find the family, express your condolences and make your excuses.
As far as going into the ceremony and the delicacy of sitting somewhere, I've always found, unless it's a family member, that it's easiest to hold back and be part of the last few mourners going in. That way all the family are seated or heading for seats and you're naturally at the back. You don't upset anyone by ending up in front of half a dozen cousins that way! Most people really don't care where they sit but some people can get a bit funny as emotions are high, so it's easier to just go in amongst the last group. Obviously if someone who knows you gestures you to go in, then do so - it's not a time to debate whether it's right or wrong with them. Go with the flow basically!
The ultimate thing is to be there for your friend and to remember it's about them and the deceased. If you think what you'd want in those circumstances, you won't go wrong as you sound like a thoughtful person.