I’d translate the sentence as «Странный выбор места для пингвина, — подумал Тим». «Про себя» (to himself) doesn’t add anything to the Russian verb except putting emphasis on the fact that Tim didn’t say it out loud. Besides, «про себя» is an ambiguous phrase as may also mean “about himself”.
Сам never means “herself”. The word for “herself” is «сама». Other case forms of сам (masculine) and само (neuter) include самого (genitive/ accusative animate), самому (dative), самим (instrumental), самом (after prepositions о, в and на). Other forms of сама (feminine) include саму/самоё (accusative case) and самой (other cases). The stress falls on the last syllable in all cases. “Myself” and the singular “yourself” can be either сам or сама, depending on the gender. All the plural forms ending in -selves translate as сами, самих, самим or самими, regardless of the gender. All of the above only applies to the meanings “without help from outside”. Another meaning of the Russian words сам, сама etc. is “without being forced”.
In the given sentence, сам means "for himself", that is, 'without any help from anybody'. This is the only possible interpretation when сам follows the verb. When сам precedes the noun/pronoun X and is pronounced at a higher pitch than X, it means "As for X [himself], he"/ "As for X [itself], it" and is used to emphasize the difference between X and some other person/thing(s). For example, "Жена у Ивана - врач, а сам он работает на заводе" = "Ivan's wife is a doctor; as for Ivan [himself], he works in a factory." Apart from the meaning 'himself'/'by himself'/'on his own', сам has the meaning 'on his own will/initiative'. A good example of this is a famous quote from a very popular Russian comedy of 1960's : "Не виноватая я - он сам пришёл!" ("Don't blame me, he came here on his own will!").
So do you think it's more likely we should use "в одиночестве" when it's something more mental/abstract? For example, он чувствует себя в одиночестве? Or maybe он тоскует в одиночестве? That's assuming either of those sentences sound natural at all...
«Он тоскует/томится в одиночестве» is a natural sentence. The same thought can be expressed by the sentence: «Ему одиноко». The phrase «чувствует себя» does not fit in the pattern. One can say though, «он чувствует себя хорошо / плохо / неважно / ужасно / прекрасно / превосходно / замечательно» or «ему тоскливо / грустно / весело / легко / тяжело / не по себе».
The phrase "thinks for himself" is inambiguouly interpreted as "thinks without asking for anybody's advice". "By himself" has two meanings, (1) alone, and (2) unaided (so the second meaning is the same as "for himself"); therefore, 'thinks by himself' sounds ambiguous. I doubt that it is widely used by native speakers.
Is the audio of 'думает' accurate? It sounds like the way Americans don't complete the 't' sound at the end of the word (the tongue is held in the 't' position, but doesn't move forward). If this is so, it would be easy for me, but I suspect the audio is just imperfect? I'm constantly trying to enunciate the 'т' at the end of words since I want it to sound correct, so it would save me a lot of work if Russian worked that way, too ;)
When т is followed by any of the letters д, т, з, с, ж, ш, н or л, you don’t need to detach the tip of your tongue from your upper teeth/gums until after you pronounce the consonant that letter stands for. So it’s similar to /ts/ in “its” or /dd/ and /tn/ in “it did, did it not?”
The only possible transitive use of the verb думать occurs in the phrase «думать думу» which means “to be deep in one’s thoughts”. Otherwise the verb думать is intransitive - in other words, it cannot take any direct objects. The word себя is a direct object when used without a preposition. Ex.: Она видит себя в зеркале = She can see herself in the mirror. Он жалеет себя = He feels sorry for himself. Он любит себя = He loves himself. Он не умеет держать себя в руках = He cannot control his emotions.