"Tiger" is a two-syllable word that starts with a T.
The second syllable.
t
/T/
C w t s
The first syllable of "photo" is stressed and the second syllable is unstressed. The lack of stress on the second syllable has the consequence that the "t" fails to be aspirated and in American English is pronounced as a flap. You can contrast this with the word "Plato", which has some low level stress on the second syllable, causing the "t" to be aspirated and preventing it from becoming a flap.
A strong syllable is a stressed syllable. This syllable is more prominent and stronger than the others, and are often found in multi-syllable words.
Sometimes, but only when the word would not be pronounceable without the extra syllable. After t or d, in English you can't have an immediately following t or d, so a vowel has to be inserted before the "-d" ending, and this new vowel produces an extra syllable.
tra
The above in phonetic notation (using - for syllable division) is [mə-stɪɹ-i-əs]. There is another possibility, which is [mɪs-tʰɪɹ-i-əs], with [s] at the end of the first syllable causing the first vowel to be slightly different, and with t now at the beginning of its syllable aspirated (with a puff of air after it), since t must always be aspirated at the beginning of a syllable in English.
/avel/
No. Thought only has one syllable. The t sound at the end might make it sound like two, but it is only one.