Was Gollum a hobbit?
Yes, beyond all doubt. Gandalf's opinion alone: "I guess they were of hobbit-kind; akin to the fathers of the fathers of the Stoors" (The Fellowship of the Ring, 62) should be sufficient to settle this, but it is confirmed in several other places. The Tale of Years (The Return of the King, Appendix B) has the following entry for the year TA 2463: "About this time Deagol the Stoor finds the One Ring, and is murdered by Smeagol." (The Return of the King, p. 368),
Since it was explained in the Prologue that Stoors were one of the three branches of hobbits (The Fellowship of the Ring, 12), it is clear that the compiler of this entry, evidently either Merry and/or Pippin's heirs (The Fellowship of the Ring, 24-25), accepted this conclusion.
In "The Hunt for the Ring" (Unfinished Tales, Three, IV) it is told that Sauron concluded from his interrogation of Gollum that Bilbo must have been the same sort of creature (Unfinished Tales, 342) (indeed, Gandalf concluded the same thing from his talks with Bilbo (The Fellowship of the Ring, 63)). The following passing reference shows that the author of "The Hunt for the Ring" accepts Gollum's hobbit origin: "Ultimately indomitable [Gollum] was, except by death, as Sauron guessed, both from his halfling nature, and from a cause which Sauron did not fully comprehend ..." (Unfinished Tales, 337).
Perhaps Gandalf's archaic diction contributed to the uncertainty. When a reader suggested that perhaps 'Smeagol's people were not "of hobbit-kind" as suggested by Gandalf', Tolkien dismissed the suggestion. He added:
With regard to Gandalf certainly says at first 'I guess' (The Fellowship of the Ring, 62); but that is in accordance with his character and wisdom. In more modern language he would have said 'I deduce', referring to matters that had not come under his direct observation, but on which he had formed a conclusion based on study. ...But he did not in fact doubt his conclusion: 'It is true all the same, etc.' (The Fellowship of the Ring, 63).
[The Letters of J.R.R. Tolkien, 289-290 (#214)]
First given as a lecture at Wycliffe Hall Oxford by Roger Rowe in 1996