Solutions for Act V Scene 1 - Common Knowledge

We are presented with four sets of clues - the first two appearing to simply refer to words with the desired number of letters. The last two set of clues appear to be somewhat obscure and it is not entirely clear what the (+n) after each clue means. However, there are arrows indicating that we should work through this puzzle in the prescribed order and, hopefully, new information will shed light on how to solve the rest of the puzzle.

The first set of answers should be readily attained.

First set of clues
A young cat (6)kitten
Desire for achievement (8)ambition
Make fun of (8)ridicule
(Of information) classified; secret (12)confidential
Outdoor grill (8)barbeque
Snowís colour (5)white
To ascend; to scale (5)climb
Wears glass slippers (10)Cinderella

The second set of clues appear to work similarly but are less specific. Some of the answers could be conjectured but we cannot be certain unless we figure out some rule to determine whether or not an answer is correct. The title suggests that we should look for something in common. Indeed, after finding a few answers we should notice that the beginning or end of an answer in the second set must match with the beginning or end of an answer in the first set - that is, they share a common portion. With this rule in mind, the rest of the clues can be quickly solved.

Second set of clues
ClueAnswerMatching answer from set 1
Answer (8)solutionambition
Customer (6)clientclimb
First (7)initialconfidential
Give insight (9)enlightenkitten
Good deal (7)bargainbarbeque
Kitchen utensil (5)whiskwhite
Small (9)minusculeridicule
Spice (8)cinnamonCinderella

We obtain the following eight common portions: cli-, bar-, cin-, whi-, -tion, -tial, -ten and -cule. It is now time to venture on to the third set of clues. We see that we have obtained 8 portions from the first two sets and that there are 8 clues in the third set, so it is reasonable to assume that each portion will correspond to a clue below. The (+n) in brackets now make sense - they tell you how many letters are to be added to a portion to create a new word. The clues below describe the answers in a very obscure manner but equipped with the above portions, our task should now be possible. Furthermore, if we correctly guess that these new words must also pair up based on further common portions then things become a lot easier.

Third set of clues
A lot like the weather (+5)climatic
And thatís not all! (+3)partial
Can you see that building block? (+4)molecule (a tiny building block)
Did that wall just move? I need to get out of the office. (+5)partition (a movable wall in an office)
Mate, letís drink on it. My shout! (+5)barstool
Relating to the big picture. (+6)cinematic
That rock doesnít look too solid. (+3)molten
Water has been going around in there. (+6)whirlpool

The new common portions are: parti- (partial, partition), mol- (molecule, molten), -matic (climatic, cinematic), -ool (bartsool, whirpool). It is now clear that we should repeat the above process to form 4 new words, with the knowledge that these new words must pair up to also share common portions. This greatly narrows down the range of possibilities. What once were (deliberately) vague clues should now make sense, if interpreted the right way.

Fourth set of clues
Certain (+5)particular (eg. a certain object; a particular object)
Grinding tool (+2)molar (tooth used for grinding food)
Processes drawn out (+4)schematic (a drawing of how a system works)
Surrounds a recess (+3)school (a recess is a small lunch break during school)

We have two new common portions: sch- (schematic, school) and -lar (molar, particular). We have one final step: use these two portions together with one extra letter indicated by the (+1). The only word which fits is scholar, a person who is quite knowledgeable.

The answer is: scholar