Reciprocal of differences calculation stymied by divide by zero exceptions

Looking for more fine structure in the data, I replotted data1.txt by days (86400 seconds).

The histogram I plotted was already rather irregular: you do not want to make it "finer". Nevertheless, you may want to observe that there is less spam during the weekends. To get the first attached histogram, I modified my previous script:
#!/bin/sh
TMP=$(mktemp -t hist_by_day_of_the_week.sh.XXXXXX)
trap "rm $TMP 2>/dev/null" 0
sort -k 1,1n "$1" | awk -v begin=1564358400 -v interval=86400 -v day=1 '
{
while ($1 >= begin + interval) {
begin += interval
day = (day + 1) % 7 }
++count[day] }
END {
for (d = 1; d != 7; ++d)
print d, count[d]
print 7, count[0] }' > $TMP
printf "set style data histogram
set boxwidth 2 relative
set style histogram
set style fill solid
set terminal pdf
set xlabel 'day of the week (1 is Monday)'
set xrange [-1:$(wc -l < $TMP)]
set ylabel 'nb of spam emails'
set yrange [0:]
set output '$2'
plot '$TMP' using 2:xtic(1) notitle" | gnuplot

Writing that modification, I realized, my previous script was wrong: it missed one email per week. Here it is again, fixed:
#!/bin/sh
TMP=$(mktemp -t hist_by_week.sh.XXXXXX)
trap "rm $TMP 2>/dev/null" 0
sort -k 1,1n "$1" | awk -v begin=1564358400 -v interval=604800 '
{
while ($1 >= begin + interval) {
begin += interval
print count
count = 0 }
++count }
END {
print count }' > $TMP
printf "set style data histogram
set boxwidth 2 relative
set style histogram
set style fill solid
set terminal pdf
set xlabel 'weeks'
set xrange [-1:$(wc -l < $TMP)]
set ylabel 'nb of spam emails'
set yrange [0:]
set output '$2'
plot '$TMP' using 1 notitle" | gnuplot

The resulting histogram is attached.

Back to my divide-by-zero problem

What you will get after "solving" your problem, which should not be solved (the only reasonable result of 1/0 is infinite, not 1), will be very irregular and essentially unreadable, even understanding the unreasonable formula for the plotted values.

bash: [: $2-p: integer expression expected

That tells you '[' (aka 'test') is interpreting that. You ask it to tests whether the string "$2-p" is numerically equal to ":0". Neither side of the equality is a number, hence the error.

You apparently want that test inside the AWK program (because p is a variable in that program and $2 is the second field, not the second argument of the shell script, what bash would understand without the single quotes around '$2-p'): the AWK action would become 'if ($2 - p) print $2 - p; else print 1'. Anyway, I repeat: your are heading nowhere, in my opinion.