What's the sixth word in these sequences?

Question

What's the sixth word in these sequences?

1. CLOUTS, OBERON, DANGER, PEOPLE, BEMOCK
2. BARBED, SCHUSS, AGENCY, HOVERS, TERROR
3. PREFAB, ARTFUL, KEEPER, INCITE, MANIOC
4. MILLED, ONWARD, STANDS, WAIVES, ALINES

and then:

5. CLUMSY, BUCKET, BROKEN, JARGON, DIADEM
6. ATRIUM, RENTAL, GLANCE, TRIPOD, SUNDAE
7. KOSHER, OOMIAK, ENDING, ORPHAN, MISHIT

Source: The GCHQ Puzzle Book

Answer 1

PARTIAL ANSWER

I am going to explain some parts that I managed to figure out myself

So, I am going to use just number 1 as an example :

We first have to arrange so that the words go down :
CLOUTS
OBERON
DANGER
PEOPLE
BEMOCK

Then, starting from the top left corner, we just get :

C
O
D

From the Top Right Corner (% sign means other insignificant letters), we get :

%%%UTS
%%%RON
%%%GE%
You go from S to T to U to R to G to E to O and finally to N
Which will give us STURGEON

As we can see,

STURGEON and COD are both types of fish but doing the same strategy from the down left corner and down right corner does not produce names of fish

This is all I have managed :D

Answer 2

This kind of looks like a really really tricky game of

Boggle.

We have 1, thanks to help from @Kevin L:

CLOUTS
OBERON
DANGER
PEOPLE
BEMOCK

Reasoning: As Kevin mentioned,

You can spell cod and sturgeon, but I noticed that there are pieces of salmon and mackerel there. If we continue the trend of starting in corners, the first three letters must be SAL, and the last two letters must be AM. This hints at the solution being SALAAM, although I’m not sure if non-English words are allowed.

For the second one,

BARBED
SCHUSS
AGENCY
HOVERS
TE RROR

Reasoning: As

You can spell Bach and Debussy, but I noticed that there are pieces of Beethoven there. If we continue the trend of starting in corners, the first two letters must be BE. I noticed that the last four letters might be related, and indeed ELGAR is formed if the last four letters are AGLE. The word here is BEAGLE.

For the third one,

PREFAB
ARTFUL
KEEPER
INCITE
MANIOC

Reasoning:

@Kevin L found that you can make parakeet and bluetit out of the top two corners. Thanks, @Kevin! I noticed then the bottom right corner should be S to make scoter, and then possibly CRE to start will make crane in the bottom right. This leaves CRE _ _ S...which leaves lots of possible words: CREAMS, CREEDS, CREEPS, CREPES, CREEKS, CREAKS, CREDOS, CRESTS...etc.

For the fourth one,

MILLED
ONWARD
STANDS
WAIVES
ALINES

Reasoning:

The top left corner gives Montana, and after considerable digging I think I can sketchily make Delaware out of the top right. The bottom left must be Hawaii (word starts with H) and with all the S and E in the bottom right corner, maybe Tennessee? This would need a TEN, so last three letters are NET, so H _ _ NET spells HORNET...?

For 5:

CLUMSY
BUCKET
BROKEN
JARGON
DIADEM

Reasoning:

The top left spells Cuba down the diagonal. If you’re allowed to repeat, I was thinking top right was Yen or Yem, but I repeated an E (is that legal?) to make Yemen. Again, this only uses diagonals so maybe we have to do that for bottom too. The I and J in the bottom left seem to imply Fiji, meaning first letter F. Starting in the bottom left, you can make ENEGA if you’re allowed to repeat — so how about Senegal, which implies a 4th letter of L and a 6th letter of S? Then we have F _ _ L _ S, which could be FIELDS, FABLES, FAULTS, FRILLS, etc.

For 6:

ATRIUM
RENTAL
GLANCE
TRIPOD
SUNDAE

Reasoning:

This one seems clumsy for me, but I can make out Argentina in the top left and Macedonia in the top right. The UST seems to imply Austria or Australia (probably the second one, since they’re all 9 letter words). Either way, bottom left corner is A. I kind of think I can form Barbados with last letters SORB, but Barbados is 8 letters not 9. If it is Barbados, then the word is either ABSORB or ADSORB (either valid).

For 7:

KOSHER
OOMIAK
ENDING
ORPHAN
MISH IT

Reasoning:

This one is super janky, but I thought of it during my latest chess match... you can make the word KNIGHT by starting in the top left corner and making knight moves. You can make the word ROOK by starting in the top right corner (skipping a few letters) and making rook moves. In the bottom left corner it appears that you can make a BISHOP with a first letter B and third letter S (and using bishop moves). In the bottom right corner you can make KING with last letter K using king moves. This leaves us with B _ S _ _ K. This involves an archaic form of a word, but I think BESEEK fits the bill here.

How do these look?