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Question 1:
Generalize procedure NuConG(N) of M18.txt to write a procedure

NuKcomponentsGraphs(N,K)

that inputs a positive integer N and another positive integer K and outputs the first N terms of the sequence enumerating the number of labeled graphs on n vertices with Exactly K componets. Make sure that NuKComponentsGraphs(N,1) equals NuConG(N) for N ≤ 6
Hint: Of course, you first need to write a procedure AllKcomponentsGraphs(n,K) by tweaking procedure AllConGraphs(n) and change the line nops(CCs(s))=1 to nops(CCs(s))=k

Are the following sequences in the OEIS? If yes, what are the A-numbers

NuConGgen(5,2), NuConGgen(5,3)

Answer 1:
#AllKcomponentsGraphs(n, K): The set of all connected (labeled) graphs on {1,..,n} with K components
AllKcomponentsGraphs:=proc(n, K) local S,s,C:
S:=AllGraphs(n):
C:={}:

for s in S do
 if nops(CCs(s))=K then
  C:=C union {s}:
 fi:
od:

C:
end:
#NuKComponentsGraphs(N, k): The first N terms of the sequence "number of connected with K components (labeled) graphs with n vertices", by BRUTE force
#Try:
#NuConG(5);
NuKComponentsGraphs:=proc(N, k) local n1:
[seq( nops(AllKcomponentsGraphs(n1, k)),n1=1..N)]:
end:

NuConGgen(5,2)
A323875		Number of labeled graphs on n nodes with two connected components.

NuConGgen(5,3)
A323876		Number of labeled graphs on n nodes with three connected components.

Question 2
Using procedures RandGr(n,K) and CCs(G), in M18.txt

write a procedure

AveNuCC(n,K,M)

that generates M random graphs on n vertices with K edges, and for each of them finds the number of components and take the average over these M random graphs. Run it several times with n=30 and M=1000 to check that you get close answers. If not what M would give such agreement?

Answer 2
AveNuCC:=proc(n, K, M) local ans, i, G:
ans :=0:
for i from 1 to M do:
#print(i):
G:=RandGr(n, K):
#print(G):
ans:=nops(CCs(G))+ans:
od:
evalf(ans/M):
end proc:

We do very close answers. 

Question 3
EstimateCutOff(n,M)

that inputs a positive integer n and outputs an estimate for the "threshold" for K, when most graphs with K edges start to be connected (say when the average number of connected componets is less than 1.05)

Answer 3
EstimateCutOff:=proc(n, M) local ans, i:
ans:=AveNuCC(n, 1, M):
i:=1:
while(ans>1.05) do:
ans:=AveNuCC(n, i, M):
i:=i+1:
od:
i:
end proc: