ibid or Ibid (Capitalisation)?
Ibid is not a proper noun, so it's not capitalized as a matter of course. (Your own question contains several examples where lowercase 'ibid' is used correctly.) Whether it should be capitalized at the start of a footnote depends on the style guide used. For example, OSCOLA uses lowercase 'ibid', whereas the Chicago and Harvard styles use the capitalized form. When used for in-text citations it is typically lowercase, however.
Finally, when used with footnotes, 'ibid' doesn't necessarily occur at the start. In books I've seen 'ibid' occurring after parenthetical remarks, such as &quot;For X, see ibid p. 50&quot;. Sometimes a single footnote is also used for multiple references, as in this example from the Physical Review style guide, where 'ibid' refers to the journal name:

J. M. Smith, Phys. Rev. B 26, 1 (1982); R. Brown, ibid. 24, 3 (1981); C.
Green, ibid. 24, 22 (1981).