There are no explicit limitations on gaining foot-based claw attacks in either D&D 3.5 or Pathfinder. Nothing says you can’t. At the same time, the overwhelming majority of claw attacks in the game are described as being on the hands/forepaws, so it certainly would be unusual. Where a natural weapon is described as being found is important in both systems, as both use a vague and implicit “logical” limitation on natural weapons that you cannot use more of them than you have the appropriate limbs for. For claws described as going on the hands/forepaws, that’s usually two.
In Pathfinder, there are no exceptions to this general concept. As Anne Aunyme’s answer points out, creatures with claws on their feet/hindpaws usually get rake attacks, not claw attacks. For birds and bird-like dinosaurs, you instead tend to see talon attacks; for example, see the velociraptor. Larger raptors like deinonychus and megaraptor even specify that they have foreclaw attacks, in addition to their talons.
In D&D 3.5, we have a lot of similar stories; the tiger and deinonychus entries make it clear that the Pathfinder versions were straight conversions without any significant changes. Tigers have rake, deinonychus has talons (and foreclaws), and so on. Even though the notorious fleshraker from Monster Manual III is described as having “a pair of 6-inch-long hooked claws” on each of its four limbs, it still has only two claw attacks and a rake.
However, Magic of Incarnum has an exception for you. The landshark boots soulmeld, when bound to one’s totem chakra (requiring a minimum of two levels in the totemist class), grants a pair of claw attacks on your hands, as well as the ability to attack with four claws, hands and feet, if you manage to jump at least 5 feet high while within reach of an opponent (a DC 20 Jump check).
- Can the claws be placed on you feet for something like catfolk/lizardfolk?
Catfolk or lizardfolk can take totemist levels and use landshark boots, but then, so can pretty much everyone else. Catfolk and lizardfolk do not have any native access to such features in either system.
- If yes to Q1 then does that increase your iterative attacks (4x claw attacks)?
Natural weapons are never iterative attacks. “Iterative” is used only for those extra attacks you get from having high BAB, that take successive −5 penalties. Natural weapons cannot be used for iteratives (barring a special exception like a monk with Feral Combat Training).
But yes, landshark boots do allow you to attack four times. It requires jumping through some hoops (ba-dum-tish), but you can.
- Does this qualify you for Multi-attack?
Yes, landshark boots would qualify you for the Multiattack feat (either system; the feat is the same in both).