Are the nuclei always in the same position in every cell?

Answer 1

When the cell is compact, the nucleus is more or less at the center. One major exception is the neuron, which may have the body (and nucleus) at the spinal cord, but the axon can go as far as the big toe.

Answer 2

The nucleus is often near the centre of a cell, but different cells can have very different morphologies:

A nerve cell has a central cell body (soma) containing the nucleus, and many peripheral extensions (typically several dendrites, and one long axon).
A columnar epithelial cell is cuboidal, with one face open to a lumen, the opposite face attached to a basal membrane, and the four sides strongly attached to neighbouring cells; the nucleus is often nearer the basal face.
A muscle fibre is actually many fused muscle cells - so it is one cytoplasm, with many nuclei spaced along its length.
An astrocyte (a type of tissue macrophage found in the brain) has a central body containing the nucleus, and many extensions.
A photoreceptor cell (like rods and cones in the eye) is cylindrical, with the nucleus at the basal end, and a highly membranous cytoplasm extending up from it.

So the answer is no.