Did you join the forward/reverse reads and then import? You may want to import as EMPPairedEndSequences and follow the steps in this tutorial for processing paired-end reads.
Yes, that's fine!
That plot does look strange for a single-end read, but aren't yours joined paired-end reads? That plot looks similar to the joined read quality plots in the tutorial I've linked to above. My guess is that the read joiner that you are using may be assigning an arbitrary PHRED quality score to the overlapping bases?
Never! 
I hope that helps!