I notice that IIø7 or IV- is often used instead of II-7 or IV to create extra pull towards the tonic. For example: if you play IIø7 in first inversion to I in second inversion, IIø7 very much sounds like a dominant chord.
Could it be said to be a dominant chord in that case?
This is ultimately the claim made by the concept of negative harmony. (See the negative-harmony tag for some other questions and answers about it.)
In short, negative harmony inverts chords around the tonic root/fifth axis. You're in C major, so we can invert chord tones around the C/G axis, which is the same as inverting around the E/E♭ axis. (Yet another way of thinking of it is to invert the pitch around C and transpose it up a perfect fifth.) And the dominant G–B–D–F inverts around this axis to create, respectively, C–A♭–F–D, which rearranged creates your iiø7 chord. And because this Dø7 is the negative harmony of G7, the theory conceptualizes it as a type of dominant.
It's also worth mentioning that this iiø7–I progression is ultimately a variation of the plagal IV–I. The A♭ is understood as mode mixture, and the D likely originated as a passing tone from C up to E.
Edit: I see that I misread the question a bit. In tonal music, a second-inversion tonic chord is ultimately an ornamented dominant. (The second-inversion tonic very often moves to a root-position dominant.) As such, this Dø7 is a pretty clear predominant that moves to dominant. However, the whole point of the predominant is that it moves to dominant, and in this sense, we can think of a predominant as a type of dominant to the dominant (just not in the standard "secondary dominant" way of, say, a D7 chord).
D,F,Ab,C have 3 tones in common with B,D,F,Ab which is considered as a rootless V7b9 chord. (The tone C would be the suspended 4th of G7 ...) Maybe that's what you perceive when playing Dm7b5 or Fm resolving to C.
Indeed Dm7b5 is often used as substitution of Dm7 in a IIm7-V7 and D7-G7 would be secondary dominant of G7. All melody lines leading from C to B can be harmonised with these 3 chords: D7 or Dm7 and Dm7b5.
No, it isn't a dominant chord. More of a subdominant. But there are plagal cadences as well as perfect cadences. If you want to say that the IV (or its variations) in a IV-I cadence has 'dominant function', as in 'a chord that isn't the tonic and leads well to it', fair enough. But that doesn't make it a dominant chord.
Not all progressions are strictly 'cycle of 5ths' functional. Consider a ♭VII - I progression. B♭ major - C major with C as 'home'. There's no useful functional analysis of that other than 'not tonic' and 'tonic. At a stretch, you could say the B♭ had a dominant function. But it isn't a dominant chord.
The half diminished chord on ii, key C, utilises D, F, A♭ and C. The same notes as iv6 - Fm6. F, A♭, C and D (both in root position). So here, a subdominant chord. Which does sound quite dominant, mainly as to get to C major, the C doesn't move, the A♭ moves a semitone to G, and the F moves a semitone to E. The semitone moves from dominant to tonic are the reasons the 'pull' is there, too. Similarly, tts has the same effect.
