Is it ok to put pictures of important goyim on the walls in the house? And what are some of the basic halachic boundaries as far as reading the books of goyis and frum philosophers.
Nechemyah Eliyahu, Brooklyn
The Rambam, in discussing the Torah prohibition of Lo Sechanem, says that one is forbidden to praise non-Jews - either their physical beauty or their behavior or their words - or that they should find favor in our eyes in any way because this will cause us to follow their ways (Hilchos Avodah Zarah 10:3, based on Gemara Avodah Zarah 20a). Perhaps hanging up pictures of non-Jews is considered an expression of them finding favor in one's eyes.
Generally speaking, one hangs up pictures of people that they love or admire. This accomplishes two things: 1) looking at the picture reminds the person of the object of their admiration, and 2) the picture is a non-verbal communication to others that he admires the person in the picture. The Rambam says (ibid.) "Lo Yiheyeh Lahem Chein b'Ainechah". It seems from his words that there is a problem here even without communicating one's admiration to others because one is expressing their admiration for the non-Jew in a tangible way by hanging up the picture.
This seems to be the case from the story in the Gemara (ibid) that Rabban Shimon Ben Gamliel recited the verse from Tehilim: "How great are Your works..." upon seeing a particularly beautiful non-Jewish woman (it was permitted for him to do that because he was praising Hash-m, not the non-Jew (see Yoreh Deah 151:14)). Maybe he was speaking to his Talmidim around him, but it is reasonable to assume that he was talking to himself. Even if he was addressing his Talmidim - i.e. the Isur is only if one expresses his admiration of the non-Jew to others - as we said, hanging a picture on the wall is a non-verbal communication to others that one admires the person in the picture. The question is whether is whether non-verbal communication - which we call Gilui Da'as - is forbidden. We hold that a Gilui Da'as does not invalidate a Get, so maybe here also only saying that you admire a non-Jew is forbidden.
I have asked several Talmidei Chachamim including Rav Moshe Sternbuch your question and none of them thought that - strictly speaking - it was forbidden to hang up pictures of non-Jews*.
Regarding your second question: The author of Chovos haLevavos gives us a basic guideline about studying secular wisdoms. He says that any Chachmah that draws us toward the service of Hash-m and toward guarding His commandments and that demonstrates Hash-m's wisdom and ability, one should and, in fact, is obligated to study; and the study of any other Chachmah is forbidden (Sha'ar Chesbon haNefesh, Ch. 3, Cheshbon #25). Ironically, there have been great rabbis over the last several hundred years - including the Vilna Gaon and the Noda b'Yehudah - who have advised against studying the first chapter of Chovos haLevavos, presumably for this very reason.
Another basic rule laid down by both the Rambam and the Shulchan Aruch is that, before embarking on philosophical inquiry, one must first be well versed in Halachah (Rambam, Hilchos Yesodei ha'Torah 2:12, Yoreh Deah 246:5 in Remah). I refer you to the introduction of the Pischei Lev to Sha'ar ha'Yichud of Chovos haLevavos for an excellent treatment of the subject of studying philosophy.
This is not a Psak Halachah