Answer
The Bible does not teach that when we go to be with the Lord we are no longer aware of continuing conditions on earth. Nor does it teach that we are aware of them. Revelation 6:10 would seem to imply that the dead remember their former lives, and that they may be aware of at least some continuing conditions on earth (e.g. the fact that judgment has not been executed against their murderers). Certainly, death does not make us omniscient or omnipresent -- the dead cannot know everything that goes on in the earth, nor can they be present here as well as in heaven.
Nevertheless, they are still conscious, and they, like we, are still awaiting the completion of the gospel. They are waiting for the final resurrection and the last judgment, and they are aware that before these things occur there is still evil in the world. They do not stop loving their families and friends, and they do not lose the freedom or ability to speak to God (i.e. to pray). They are still "saints" (e.g. Rev. 11:18). I would assume based on the information that the Bible does provide that departed saints still pray, and that they are able to petition God on behalf of people still on earth. On the other hand, the Bible does not indicate that they can hear us talk to them, or that they know all that much about continuing life on earth. Thus, it would seem to me that their prayers would primarily be based upon knowledge they acquired during their lives on earth (supplemented perhaps by talking to others who died later, or to angels, or perhaps by God?), and that they would not hear us when we asked them to pray for us.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.