Nikosandros said:
1) Is the controller required to have line of effect to the creature?
It appears so, from the quote posted above.
Nikosandros said:
2) What is the range of the conjuration? The creature can only be conjured in an adjacent space, but does this mean that it must always remain adjacent?
Again, as posted above, the RAW seems to indicate that it can range as far as the owner's line of effect. This creates the odd circumstance in which, for example, it falls down a pit-trap, and dissappears before hitting the bottom because it is out of the line of effect.
Nikosandros said:
3) Are those creatures capable of thought? Do they keep their memories when they are conjured again?
I couldn't find anything RAW about this, so I'm going to opine that it's within the purview of any particular campaign's fluff.
Nikosandros said:
4) Does the death of the conjuror automatically make the creature disappear?
From the passage quoted above, it appears so.
I find the following passage, also under the conjuration keyword, to be mildly confusing in relation to some of the figurines.
Unaffected by the Environment: Terrain and environmental phenomena have no effect on the conjuration. For example, a conjuration that is an icy hand functions in an inferno without penalty. The conjuration does not need to be supported by a solid surface, so it can float in the air.
This clearly states that the figurine can walk off a cliff, or even a tree branch, and float in mid air. Most of the figurines quite obviously walk on a surface. Some have a climb speed or a fly speed. Allowing all figurines to float in mid air seems disrespectful, to put it mildly, of those that fly. So, much as this sounds retarded to me, I have to ask, per RAW:
5) Would you allow an Onyx Dog to float or walk through the air?
Also, two questions regarding the temporary hit points of the figurine. To provide some background, figurines cannot be healed, and when they are called, they last 8 hours, and their owner can spend a surge to give them temp HP equal to the owner's surge value. Per the rules, temp HP dissappear when someone takes a short rest (PHB p 294).
6) Can the owner of the figurine not rest while the rest of the party does?
7) Can the figurine not rest while the owner does?
Finally, a question about flanking. The passage quoted below is in the introduction to figurines. I remember reading somewhere that to flank, a creature had to be able to make opportunity attacks, or somesuch. Whatever it was, I walked away with the impression that if an entity was not dangerous on its own, it couldn't provide a flanking bonus.
AV p180 said:
Conjured creatures lack basic attacks and therefore cannot make opportunity attacks.
8) Does this mean a figurine cannot flank in melee?