My hamster is in the habit of opening his cage by himself and escaping.
My little sister borrowed my scissors without asking me.
この場合、次のような言い方ができますよ。
ーMy hamster is in the habit of opening his cage by himself and escaping.
「うちのハムスターは勝手にケージを開けて脱走する癖がある」
to open his cage by himself で「ケージを勝手に開ける」
ーMy little sister borrowed my scissors without asking me.
「妹は私のハサミを勝手に借りた」
to borrow my scissors without asking me「勝手にハサミを借りる」
ご参考まで!