First issue, you can try to use a Macro in the Search Mode that looks to the URL parameter, something like
{% if(!string.IsNullOrWhiteSpace(searchtext)) { return "The mode"; } else { return "ExactPhrase"; } |(identity)GlobalAdministrator%}
Sorry i forgot what the mode is for the non exact phrase (you may have to inspect the normal drop down so you can find the value).
For the second issue, again you may need to use Macros to clean up the value that comes in, for Lucene.net you need to use the escape character \ before any of the following reserved characters: && || ! ( ) { } [ ] ^ " ~ * ? : \
So use a macro such as {% MySearchValue.Replace("\"", "\\"") |(identity)GlobalAdministrator%}