Thanks, Sensini. Do you know also the dates of the two matches between Austria and Czechoslovakia? We have the following information:
30-04-1960 Czechoslovakia-Austria 2-1
07-10-1959 Austria-Czechoslovakia 0-0
but we aren't sure about it.
Luca, both dates are correct.
I found that the Dutch FA requested the FIFA to investigate the amateur-status of the Austrian players in Nov. 1959 (see http://kranten.kb.nl/view/article/id/ddd%3A010687910%3Ampeg21%3Ap005%3Aa0102). In June 1960 the FIFA concluded Austria indeed fielded non-amateurs, but because Austria was already eliminated by that time, there were no direct consequenses (see http://kranten.kb.nl/view/article/id/ddd%3A010459867%3Ampeg21%3Ap008%3Aa0134).
One of the other matches in that group:
6 Apr. 1960 Czechoslovakia - Hungary 1-2 (HT 0-1) Brno
Date unknown: Hungary - Czechoslovakia (at least after 6 Apr. 1960)
Some other matches:
17 Apr. 1960 Tunesia - Sudan 2-0 (HT 1-0) Tunis
End of Aug. 1959 Afghanistan - India 2-5 Kabul (see http://kranten.kb.nl/view/article/id/ddd%3A010501044%3Ampeg21%3Ap003%3Aa0031)
Afghanistan - India scheduled for 5 Dec. 1959, but Afghanistan withdrew (see http://kranten.kb.nl/view/article/id/ddd%3A010405920%3Ampeg21%3Ap008%3Aa0112).
Both matches Japan - South Korea played in Tokyo (see http://kranten.kb.nl/view/article/id/ddd%3A010405955%3Ampeg21%3Ap008%3Aa00930
14 Apr. 1960 India - Indonesia 4-2 (HT 2-1) Calcutta
30 Apr. 1960 Indonesia - India 2-0 (HT 0-0) Jakarta
30 Apr. 1960 South Korea - Rep.China(=Taiwan) 1-0 Taipeh (abandoned after 35 min., see http://kranten.kb.nl/view/article/id/ddd%3A010473810%3Ampeg21%3Ap004%3Aa0055)
22 Dec. 1959 second leg Peru vs Uruguay 3-2 (HT 2-1)
Date unknown: first leg Peru vs Uruguay, and who played at home first?
16 Apr. 1960 Peru - Mexico 1-0 (HT 0-0) Lima
19 Apr. 1960 Peru - Suriname 3-1 (HT 0-1) Lima
All this info I found by using http://kranten.kb.nl, the online archive of Dutch newspapers (still expanding).
Who knows similar services in other countries?