×
0 1 2 5 6 8 => all representable "more or less as is" with O I Z S b B
3 9 => representable backwards with E P
4 7 => representable upside down and backwards (or rotated 180 degrees if you prefer) with h L

of course, one could argue, that since it's your puzzle, your interpretation wins, but given that you gave us inconsistent data: namely I Z S are the same as the numbers, E is 3 backwards, H is kinda like 4 but with an extra line, unlike "h" which at least has the same strokes as the commonly-handwritten open-top 4; I guessed from the 3:1:1 ratio that "plain resemblance" is preferred, thus "b, B, O", backwards is next best, thus "P", and finally "L" for 7 because nothing else is even close (and I forgot 7 anyway somehow until Maurog reminded me )

×I'm presuming the puzzle was asked with Shell Oil in mind.

×You need to determine who is the Guard or Stalwart. Once you've done that, you only need to ask one question -- "is the Lucky Greckle in Fetch the Pie? -- to one or the other. Who you are speaking to will determine where you look.

Okay, so minimum number of questions...

There are six possible ways they could be standing:
Combo 1: GNS
Combo 2: GSN
Combo 3: NGS
Combo 4: NSG
Combo 5: SNG
Combo 6: SGN

For simplicity's sake, I'm going to call them Leftie, Middleman and Rightie.

Ask Leftie "Who are you?"
Ask Middleman "Who is Leftie?"
Ask Rightie "Who is Leftie?"

Possible Responses:

Once you sort these out there are 19 distinct answers, which fall into 4 Groups. Those answers follow, along with what can be determined from them:

Group 1 - Responses that determine everyone’s identity:

Group 2 - Responses that determine who is a Stalwart or Guard:

Group 3 - Responses that don't determine anyone's identity for certain, but narrow Leftie's down to two possible characters:

Group 4 - Responses that do not identify anyone or narrow down Leftie's character:

So from this we see that it is possible to identify either a Guard or Stalwart with only three questions. Once that happens, you need ask only one more question: Is the Lucky Greckle in Fetch the Pie? Since you know if you are addressing the Guard or the Stalwart, the answer you get will tell you where to look.

Answer: 4 questions are the minimum number of questions required to determine in which hold the Lucky Greckle is hidden, but only if you were lucky enough to get a response that fell in Group 1 or 2.

Just because I had nothing better to do, I worked out the maximum number of questions required.

The maximum number of questions required to determine where to look is 10.

Note: I'm sure that even if this correct, there was probably a much simpler way to do this.

×two

×Ask each one "what would you say if I asked you 'Is the Lucky Greckle in Nobard's Hold'?", go by majority consensus.

×Ask the one on the left, "Do the statements that you are a Stalwart and that the one in the middle is a Negotiator have the same truth-value?"

Reasoning: if you ask a Stalwart or a Guard "Do the statements that you are a Stalwart and X have the same truth-value?" then if he says yes, X must be true, and if he says no, X must be false. So a yes-answer to the question means that if the one asked is a Stalwart or Guard, the one in the middle is a Negotiator. In other words, the one on the right is definitely not a Negotiator. Similarly, a no-answer means the one in the middle is definitely not a negotiator.

Either way, you have one is who is definitely not a Negotiator, so you can ask "Do the statements that you are a Stalwart and that the Lucky Greckle is in Nobard's Hold have the same truth-value?" and a yes to the second question means it is in that hold, while a no answer means it's in Fetch the Pie.

×On every cycle, each tarstuff either loses 1 layer or gains 1 layer, so their parities must always change. That means that the parities of the differences between any two tarstuffs are constant. The difference between tar and mud has a parity of 1, which means that they cannot both be 0 at the same time. Thus gel cannot be the only tarstuff left. Similarly, mud and gel cannot both be 0 so tar cannot be the only tarstuff left. Therefore the answer is mud.

×The key to this problem is handling 2's and 3's separately.
Note this special grid:

2 0 1
0 1 2
1 2 0

In this grid, every row, column, and long diagonal adds to 3.
Using 3 to each number's power gives:

9 1 3
1 3 9
3 9 1

Here every product is 27.
Reflecting the original grid and taking 2 to each number's power gives:

2 1 4
4 2 1
1 4 2

Here every product is 8.
Multiplying the grids gives:

18 1  12
4  6  9
3  36  2

which, after some shuffling around:

3  4 18
36 6 1
2  9 12

seems to work.

×

1---2---3---4
 \   \     /
  5   6---7
   \ /   /
    8   9
     \ /
      10

Last three connections not drawn in the above diagram for simplicity:
1 and 9
4 and 5
3 and 10