Question #1: Will we have relationships in heaven and will they be the same as those on earth?

The Bible gives us every indication that in the new heaven and new earth we will definitely know one another and be in perfect relationships. What God created when He made us and stamped His image on us will not be "un-created" when creation is redeemed. What we now know and experience (except sin) will be carried over after the resurrection in its perfected, redeemed state. And that includes relationships. But that means those relationships will certainly be different than they are now. Jesus himself said that even marriage would be redefined at the resurrection. See Matthew 22:23-33. Some people find this discouraging because they are hoping to have the exact same relationship with their spouse, children, family, etc. in heaven. And I certainly can relate to that feeling. Here's a simple illustration that might help:

Remember when you were an infant and your parents first introduced you to the concept of "dessert." They gave you an animal cracker. That was the sweetest, most delectable treat you'd ever tasted. And dessert was awesome! You looked forward to your dessert of animal crackers after every meal. But growing up, you noticed the adults around you never enjoying animal crackers. In fact, when dessert time rolled around they seemed to crave these things called hot fudge sundaes. Never once did they complain about not getting animal crackers. It seemed as if the sundaes had now replaced animal crackers for them which made no sense to you as an infant because - "What could be better than animal crackers???"

The point is this: The pleasure and fulfillment in the things of this life we now experience is our only frame of reference. To imagine something more fulfilling and more satisfying is nearly impossible. But the fact is that in the new heaven and new earth, our newly discovered relationships, pleasures, sensations, thoughts and activities will so far outweigh our current ones that they will exclude them all together. We will never long for "the way things used to be" because our redeemed state will make this world a fond but distant memory. We will keep our relationships and experiences. But they will be perfectly renewed and redeemed.