1)
As the site Majestic-san provided shows, no.
2)
As mentioned in the site, the most common definition of tadōshi/transitive verb is "verbs that take を as the object marker".
Notice that not all verbs that have an object are transitive verb. For instance, お金が要る means "I need money", thus, お金 is actually the object in meaning, but 要る is an intransitive verbs because が is used to indicate the object.
Similarly, some action verbs that take を are intransitive verbs. を indicates the location of movement in the following verbs.
e.g.
廊下を歩く
道路を走る
坂道を登る
橋を渡る
空を飛ぶ
Also, を indicates the departure point of movement in some intransitive verbs.
e.g.
故郷を離れる
家を出る
大学を出る
These exceptions are not so many, so you can think that verbs that are used with を are usually transitive verbs.