Hey hey!

I'll be flying in to Frankfurt from Singapore and then according to my itinerary, as planned by the airline I'm taking Lufthansa, I'm required to take the ICE train to Stuttgart. It is my first time taking this train and further information about where should I go and what to do is limited.

1 - Do I get out of the immigration and the airport then to the train station?
2 - At the train station am I required to check in any baggages? Will it be fine if I just bring everything with me on board the train cabin?
3 - Are there any stops in between the train ride between the Frankfurt airport to Stuttgart HBF railway station?

My train number is LH 3634

Hope to hear from you soon