Enter birthdates on the Amtrak site? Not necessary in my bookings over the past decade, but perhaps I have one already stored in my profile or this only applies to trips/classes with alcohol served?
While there is some ID checking and TSA presence around train travel, especially in the Northeast (the overnight from Boston to DC last week involved passing a dog sniffing for drugs or explosives or something), it's nothing like air travel and takes seconds, not minutes/hours and invasive searches. For me, that's part of the charm.
For this particular itinerary, the best experience is near the Summer Solstice, for best probability of daylight by the time you hit Mt. Shasta. Although the trip in winter has its own charms, especially in rural southern Oregon, far from freeways, surrounded by towering snowdrifts.
Be prepared for significant delays; freight still gets priority, and only a single track is available for parts of the journey.
35 hours is a long time, as you say. A somewhat abbreviated version of the essence of the experience is available from the Bay Area to Portland, although the timing is such that you miss dinner unless it is running very late. ProTip: Northbound, disembark in Eugene and enjoy cultural activities there, and continue the next morning via fast tilting Cascades train up to PDX/SEA/Vancouver. Southbound, you can do a similar breakpoint at dawn in Sacramento, and continue down to San Jose via Capitol Corridor. Eastbound on the California Zephyr, I've found it sometimes worthwhile to board the Capitol Corridor in Berkeley, change to the Eastbound bus and check luggage in Sacramento, zip over the Sierras to Reno on the connecting bus, and then get a few hours there before boarding in the evening.
Do shop the Amtrak site for last-minute and advance-discount fares and sales, with similar fare algorithms to the airlines; prices tend to go up significantly in the last few weeks/days and only limited quantities of the cheapest seats are offered per train. The best deals are the last-minute specials, although they don't allow adding a sleeper unless one happens to be available onboard.
AAA members get a 10% discount on the train (not lodging/meals) part of the fare, and a National Association of Railroad Passengers (NARP) membership can be a good value, offering a similar discount plus "Amtrak Guest Rewards" points, and you help support lobbying to keep Amtrak funded and viable.