1. 

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:=proc(N,K) local n1:
[seq( nops(AllKcomponentsGraphs(n1,K)),n1=1..N)]:
end:

NuKcomponentsGraphs(5, 2) = [0, 1, 3, 19, 230] = A323875
NuKcomponentsGraphs(5, 3) = [0, 0, 1, 6, 55] = A323876



2.

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

AveNuCC(30,50,1000) =
1.841000000
1.824000000
1.782000000
1.794000000
1.753000000
1.838000000

At M=1000, the averages vary. At around M=10000, the numbers are closer with usually less than a .1 difference (1.801000000, 1.810500000, 1.808900000,...).


3.

EstimateCutOff:=proc(n,M) local i,j,max,ans:
  max:=binomial(n,2):
  for i from 1 to max do:
    ans:=0:
    for j from 1 to M do
      ans:=ans + nops(CCs(RandGr(n,i))):
    od:
    if evalf(ans/1000) < 1.05 then
       i:
       break:
    end if:
  od:
end: