Bibliography items should appear in the project tree if you use \bibliography. To get this feature working with \addbibresource, you need to add a WinEdt input directive. Open up the options interface (Options... > Options Interface) and go to Navigation > Input Directives. This will open the Input.ini script. After the \bibliography directive, add this new entry:
DIRECTIVE="\addbibresource??{??}"
EXTENSION=".;.bib"
PATH="%P;%p;%@('BIBINPUTS');"
Save and reload the script. Once you rebuild your project tree, the bibliography items should appear.
A menu containing the items should popup when you add braces to \cite or any natbib citation command. With biblatex you could simply use the package option setting natbib=true. Otherwise this feature can be extended to biblatex citation commands by further modifying WinEdt option scripts. From the options interface go to Delimiters... > Active Strings. After the \cite?{ string in ActiveStrings.ini add the following.
STRING="\?cite?{}"
ENABLED=1
FILTER="TeX"
ACTION="[Exe('%b\Macros\Active Strings\Cite.edt');]"
DBL_CLICK_ENABLED=1
DBL_CLICK_FILTER="TeX"
DBL_CLICK_ACTION="[IfNum(%c,%x,'<','SwapCaretSelect;');CharRight(2);Exe('%b\Macros\Active Strings\Cite.edt');]"
STRING="\?cite?{?},,"
ENABLED=1
FILTER="TeX"
ACTION="[Exe('%b\Macros\Active Strings\Cite-cont.edt');]"
STRING="\?cite?{?,,"
ENABLED=0
FILTER="TeX"
ACTION="[Exe('%b\Macros\Active Strings\Cite-sel.edt');]"
STRING="\?cite?{?}"
FILTER="TeX"
ACTION="[GDIShow;GDISetPage('Bib','%?');]"
DBL_CLICK_ENABLED=1
DBL_CLICK_FILTER="TeX"
DBL_CLICK_ACTION="[IfNum(%c,%x,'<','SwapCaretSelect;');MatchDelimiter(1,1,1);CharLeft;GDIShow;GDISetPage('Bib','%?');]"
STRING="\?cite?{"
FILTER="TeX"
ACTION="[Relax;]"
DBL_CLICK_ENABLED=1
DBL_CLICK_FILTER="TeX"
DBL_CLICK_ACTION="[IfNum(%c,%x,'<','SwapCaretSelect;');CharRight;GDIShow;GDISetPage('Bib');]"
From the options interface, go to Navigation > Gather. In Gather.ini add alternatives for the \cite{?} and \cite[?]{?} items. For example:
ITEM="\cite{?}"
ALT="\nocite?{?}"
// NatBib extension
ALT="\citep{?}"
ALT="\citet{?}"
ALT="\citealp{?}"
ALT="\citealt{?}"
ALT="\citefullauthor{?}"
ALT="\citeauthor{?}"
ALT="\citeyear{?}"
// biblatex extension
ALT="\autocite?{?}"
ALT="\Autocite?{?}"
ALT="\textcite?{?}"
ALT="\Textcite?{?}"
...
Getting the popup feature working with multi-citation commands that generate qualified citation lists (e.g. \cites[<prenote1>][<postnote1>]{key1}[<prenote2>][<postnote2>]{key2}), will probably require a new active string macro. I ditched Windows awhile back so I never got around to writing any myself. The existing macros Cite.edt, Cite-cont.edt and Cite-sel.edt provide some examples. These can be found under Advanced Configuration > Active Strings from the options interface.