1. How many of them contain at least one '1'?
2. If I wrote them out in one long line, how many 1 digits would there be?

Part 1:  612,579,512

Reasoning (In Perl):

my $i=0;
for (1..1000000000)
 {
 $i++ if (/1/);
 }
print $i;

Part 2:

I am just taking a stab at this, and I am not typing the answer here because of accuracy reasons, but I believe it is:

300^1,000,000 +  300^1,000 + 1

The answer is 4955 digits long, but I cant seem to find a calculator to compute that accurately