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Answering the title question, your tf tree looks okay to me; it is similar to what we use in most of our mobile bases.

Regarding the absence of a map:

• Have you tried moving the robot around? I'm not sure how hector works, but it may not be getting "enough" info from a stationary sensor to warrant publishing a map;
• Have you taken a look at rosnode info for hector? Are you subscribing to the correct map topic in rviz?

Your internet connection should not have much of an influence you ROS as long as:

• Everything is running on a single machine;
• The master is routing through localhost or 127.0.0.1.

Best of luck!