I've experienced this as well (all the issues you mention). All should be fixed. It might be an idea to raise some bugs: https://bugbase.adobe.com/.
If you post the bug references back here, I'll vote for 'em.
Here are the bugs I created... would be great if they got votes. I cannot use CFB 2 without fixes to these problems because I rely on CTL-F to work correctly. I'm not sure how these things passed QA... it's a far departure from the way std. eclipse and CFB 1 work. At the very least, we need a patch or workaround that will allow us to turn off ColdFusion Search and use the built in eclipse Find dialog.
ColdFusion Search "Current Document" scope does not work when selecting a different file
ColdFusion Search does not save settings
There is no way to disable multiple ColdFusion Search dialogs
Good stuff. Voted for all three.