1) If one is standing in front of a statue or a cross or other symbol of Avodah zarah, it is prohibited to bow [and even to daven, or learn] while facing them, rather make sure to [daven, learn and] bow to the side. (This is common when davening in hospitals, airports, lounges, hotels and other public areas).
Even if the objectionable object is behind a glass, it is still prohibited to [daven, learn and] bow in its direction.
Ideally, if you have no other place to daven, the objectionable item should be covered [with a double covering, if possible]
2) If there is a picture or painting that contains within it a cross or similar item, even though it wouldn’t be considered bowing to a cross, it is still best to be stringent and not [daven, learn or] bow in the direction of such a picture.(Psak of Rav Chaim Kanievsky Shlita)
Some Poskim take this a step further, and prohibit davening in a room that contains in it books, newspapers or other items that contain within them words of Apikorsus (heresy) and Minos (anti-Torah ideas). (See Shu"t B’Tzel HaChachma Vol. 2 Siman 84, and Sefer Derech PiKudecha Mitzvas Lo Ta’aseh 11 in the footnotes). Similarly, it is forbidden to daven in the presence of a television that is turned on, as it is the same (and probably worse) as a book containing Apikorsus lying in the room (Piskei Teshuvos Siman 95 footnote 60)
If one is in a hospital and cannot move to a room where these impure texts are present, it is best to turn and daven in a different direction, even if by doing so they will be davening Shemona Esrei towards a different direction than "Mizrach" (East).
If they cannot turn away, the eyes should be closed, or covered by the Siddur, and the head bent down. (Sh’Arim Metzuyanim B’Halacha Siman 18:7 quoting Shu"t Atzei Chaim and Shu"t Chelek Levi)
Reader’s Question:
[You wrote that it is ideal to say Birchos haTorah before reciting Krias Shema].What about if [you didn’t yet say Shema and] it’s right before Sof Zman Krias Shema and if you say Birchas Hatorah you will miss Zman Krias Shema?
My Answer
Although it’s ideal to recite Birchos HaTorah before reciting Krias Shema, in the situation you described, one may recite Krias Shema before Birchas HaTorah in order not to miss the Zman. The Shu"t B’Tzel Hachachma Vol. 1 Siman 1, maintains that only the first 2 Parshiyos are said in such a case before Birchos HaTorah, and the third Parsha must wait until after the Brachos are recited.
Our holy sages, the Chazal tell us תנא דבי אליהו כל השונה הלכות בכל יום מובטח לו שהוא בן עולם הבא, שנאמר הליכות עולם לו, אל תקרי הליכות אלא הלכות - one who studies [at least two] Halachos daily is assured a portion in Olam Haba - the world to come. (:מגילה כ"ח )