My two questions:

1. Should I get a 4-way coax splitter with each output at 7dB and
terminate the unused output? This would leave an output free for future
expansion in Room 4. I saw such a splitter at Radio Shack. Is there a
better brand?
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Yes & no...if the splitter is a 1 gig splitter, it'll work. Don't use the
900mhz splitters...they'll work...so so...but you'll get better signal
through the 1 gig splitter, and they are not expensive...I get them at Home
Despots...about $5...can't remember if they are Ideal or RCA branded...you
will probably not need any signal amps...unless your really working with a
bad cable company. They take special care to boost their signal throughout
their network, and really try hard (in my area with Comcast) to pump good
signal to their users.
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2. Should I terminate the cable in the unused Room 1?
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Always terminate unused coax ends tied to the distribution network.
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Rich