Given the lack of response here I'm going to throw up my own answer with the best information I've found.
1) If the construct familiar has the mauler archetype, when it grows to medium will it gain "bonus HP" as per the construct traits?
This mostly comes down to which is more specific, between the familiar rules setting the HP to half of your own and the construct traits adding the bonus HP. It seems that the familiar rules would be more specific, as they are shown in other cases to generally override basic creature properties/traits.
2) Based on this FAQ, am I correct in assuming that in PFS a Tinkerer can pay for construct upgrades via these rules once the familiar upgrades at level 6?
As best as I can tell, yes, however I haven't locked down to what extent they may be used, or if there is some other listing of construct upgrade rules. It seems most likely that only the three options listed under the Construct Modifications header are available.
3) If a Tinkerer takes the Tumor Familiar discovery, will the clockwork familiar gain the ability to attach to his body for fast healing?
While it seems strange flavor wise, the answer does technically appear to be yes.
4) Once the familiar upgrades to a Clockwork Familiar and no longer has a slam attack, does the tinkering option that increases slam damage add a slam attack or does it do nothing?
The general consensus on this is that it would not add a slam attack, as the wording does not say it gains a slam, only that its slam does 1d3 damage, so if the creature doesn't already have a slam attack then the tinker does nothing.
5) The Clockwork Bond ability has a line that says, "Unlike most familiars, a clockwork spy does not grant special abilities to its master." Does this only mean that it doesn't grant a usual familiar skill bonus, or does it extend to things like the bonus Alertness feat and other abilities from the normal familiar rules?
The general consensus here seems to be that it only refers to there being no skill bonus.
There unfortunately does not seem to be much by way of hard RAW answers for these questions, and are mostly left up to interpretation.