Never been to California and wondering when is the best time to go to DL? We were thinking around June 28- July 5 or anytime in June. I hope to go when everything is up and running but not so crowded to not enjoy it

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"Best time" means different things to different people. In my book that is the best time to go, one of the reasons being that everything is up and running by mid-June (no rides in refub except long term refurbs), the shows are all at maximim frequency and the parks hours are maxed out.
Here is a link to a recent question about June trips:
www.disboards.com/showthread.php?t=1608280. See my post #2 specifically about grad nights.
As far as heat, it depends on where you are from. From this link: "Getting The Most Out of a Summer Visit To DLR"
www.disboards.com/showthread.php?t=1345319
www.wrcc.dri.edu/cgi-bin/cliMAIN.pl?ca0192 (Period of Record: 8/1/1989 to 12/31/2005)
June: Average High 80.2F (26.8C), Average Low 60.5F (15.8C)
July: Average High 84.4F (29.1C), Average Low 63.7F (17.6C)
August: Average High 86.8F (30.4C), Average Low 64.2F (17.9C)
Yes, SoCal does get heat waves as attested by the recent tragic fires, but the average high temperatures are IMO ideal. On my last three summer trips (in late June and early August) it has neve gotten above 85 degrees. When we went on a July trip in 2000 it did reach the low 90's. One big difference from WDW is that the humidity is a non-issue.
In any case, follow the advice in "Getting The Most Out of a Summer Visit To DLR" above and the heat should not be a big issue for you.
Here is another recent link to summer temperatures
www.disboards.com/showthread.php?t=1620814
I would second advice to try to avoid July 4, especially when it is a three day weekend.
One more question can you use your WDW annual pass, I'm sure not but I want to be positive?
Nope. You can use unexpired WDW tickets but not APs.
Also check out "A DLR Guide for WDW Vets"
www.disboards.com/showthread.php?t=1162599