Can a Synthesist Summoner wear Boots of Speed and still have his eidolon make claw attacks with those feet? While rational thought would say that wearing boots would cover up any claws on the hind legs, the wording for Synthesist states, "The synthesist wears the eidolon like translucent, living armor." So this would then be putting on a claw like armor over the summoner's boots??
You probably can.
It seems that it is intended that you can use your eidolons natural attacks regardless of any gear your character is wearing. As you noted, the Synthesist text states that "The synthesist wears the eidolon like translucent, living armor." I'd interpret this as wearing the eidolon, including his claws, over your normal gear. Thus allowing you to wear boots (or gloves or any other gear) and still make your claw attacks.
There is no RAW supporting that you can use the claws while "wearing" the eidolon, nor is there any RAW supporting that you can't. Thus, talk to your DM.
On a sidenote: If your DM rules that you can't use the claw attacks because you are wearing boots, you could always try to get "Anklebands of Speed". They would still occupy the same magic item slot (feet), and thus cost the same amount, while not interfering with your claw attacks. Though this would technically be a custom magic item.
As long as you are humanoid, you shouldn't have a problem with the format of your hands and feet.
While wearable wondrous items typically resize themselves to fit a creature trying to wear them
From the description of Hand Slot on the magic item chapter, we got:
The hand slot consists of gauntlets, gloves, and other items that can be worn on the hands.
Anyone can use a hand slot wondrous item unless specified otherwise by the item's description.
Note that non-humanoids will have different body slots than humanoids. So they might not have hands. Your claws are natural weapons, but you still got your hands, which is the requirement for hand slot items.
So, unless the item's description disallow a character to wear it if they got claws, they are allowed to use it by the rules.