For items 1&2, you need 70-200mm f/2.8 VR as 多年以前 suggested. For NFL, you need 1.4x and/or 2.0x teleconverter on top of this lens.
For item 3, 旅游时喜欢拍远景: the above lens. For landscape, you need a wide angle lens, your choices are: Nikon 17-55mm f/2.8 (~$1200) or Tamron 17-50mm f/2.8 (~$450) or Sigma 18-50mm f/2.8 (~$400).
For item 3, 旅游时喜欢拍远景: the above lens. For landscape, you need a wide angle lens, your choices are: Nikon 17-55mm f/2.8 (~$1200) or Tamron 17-50mm f/2.8 (~$450) or Sigma 18-50mm f/2.8 (~$400).