Can our dead loved ones see us from heaven? Can they know what we are doing on earth?

There is no evidence in scripture that they can watch our movements on any continual basis as if through a window. Practically speaking, I doubt that they would have this kind of knowledge. After all, heaven is separated from sin and nothing can enter that defiles (Revelation 21:27And there shall in no wise enter into it any thing that defileth, neither whatsoever worketh abomination, or maketh a lie: but they which are written in the Lamb's book of life.
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To watch us in all our sins and our sorrows would bring tears to a place that has no tears.

However, there is probably a limited knowledge of things on earth. Jesus says in Luke 15:10Likewise, I say unto you, there is joy in the presence of the angels of God over one sinner that repenteth.
See All..., "Likewise, I say unto you, there is joy in the presence of the angels of God over one sinner that repenteth." This joy is in the presence of the angels. It does not say it is the angels that rejoice; only that it is in their presence. This may be the Lord Himself rejoicing or it may be those who knew and loved the ones who repent. At any count, I do not believe that a saint would be in the presence of such rejoicing and then be shielded from knowing its cause. This makes me think that God will indeed reveal spiritual victories of loved ones to those in heaven.