Hakone Round Trip

Can I travel the Hakone Round Trip in reverse order, eg. Gora to Hakone-Yumoto by Tozan Railway? Where can I get the time schedules for all transport in the round trip, ie. Tozan rail & bus, cable car, ropeway and boat. I do not want to get stuck in the middle of the course especially in the evening.

Of course! It is entirely up to you in which direction you prefer to travel.

Where can I get the time schedules for all transport in the round trip, ie. Tozan rail & bus, cable car, ropeway and boat.

Rail and cable car:
http://www.jorudan.co.jp/english/norikae/

Ropeway:
http://www.hakoneropeway.co.jp/foreign/index.htm

Sightseeing Boat:
http://www.hakone-kankosen.co.jp/gaikoku.hp/index.htm

The bus timetables are available in Japanese only. But buses along the main lines typically operate every 10-30 minutes from around 6:30am to around 9pm:
http://www.hakone-tozanbus.co.jp/