I'm thinking in terms of: We three dimensional humans can draw a square on a paper--that is the squares universe. It could grow bigger if we attached more papers and drew more squares. If it were possible for a 4 spatial Dimensional element/living object with cognitive abilities to have contact with our world, how could it directly affect our individual lives? What are the limits to what it could do?
My best guess would be uninterrupted freedom to arrive at every time period; since the theory of relativity teaches that only objects without mass can travel at the speed of light and above. Mass is the measurement of atoms an object contains, so since we can only measure 3D atoms, their mass would likely not apply here.
EDIT: By 4-D organism, I meant spatial dimensions, not our perceived four dimensions of x,y,z + time. This organism likely has organs and physical features modelling R4. Tesseracts are commonplace "boxes" in the universe this organism comes from, among other regular objects implementing that interface. Let's say it gains access to our world through its civilisation's version of 3D glasses or perhaps telekinesis, it can see or communicate with a few spiritually advanced people who can perform astral travel and other metaphysical exercises. Furthermore, if it were probable for it to have a shadow, would its resulting image be some sort of hologram of the observer?
EDIT2: Someone in the comments mentioned something about this organism having mass just like us. To elucidate on my earlier point, what we know as mass is the measurement of particles. Now, we measure these particles in terms of electrons, protons and neutrons. Let's say there are other particles which we "overlook" because of our limitations. In our universe, this organism's mass will be unable to be measured in grams (which leads to my earlier conclusion that it has no mass here, hence can move at lightning speed). I hope this makes it clearer.