- Yes, kids can earn FF miles just like everyone else. Sign 'em up as needed. I use my own email address for all of them...only downside is that when an airline spams me, I get spammed 4 times.

Although occasionally it's enlightening to get both an elite-targeted email alongside the same announcement to non-elites. Most program "enhancements" are bad news...sometimes fun to see how they've tried to polish the turd for the non-elites.
- All accounts for all U.S. programs that I'm aware of are individual. You and your wife would have separate SPG accounts, separate Delta accounts, separate HHonors accounts, etc. The ability to merge two HHonors accounts died 5-7 years ago. Some programs (Marriott maybe?) will allow two people at the same address to pool points if needed to redeem a single large award but I honestly haven't done this myself. BA Avios has a very detailed Household Account program with some significant benefits and significant restrictions: it'd be best to read their FAQ if that's of interest to you. For Americans, it's primarily meaningful if a husband and wife
both have 100,000+ Avios from the Chase signup. Can obviously also be meaningful if both of you are flying a ton of BA or otherwise generating Avios.
- Typically, the name on a hotel reservation is the account that earns the points. What I was alluding to upthread was the fact that your wife would be the primary cardholder on the SPG Amex credit card, thus I believe (but am not 100% sure) that SPG and Amex would require those points earned from credit card spending to go into an SPG account for her. You would have a secondary card in your name, but the points flowing to her account.
Example: Mrs. Smith is the primary Amex cardholder. Mr. Smith is the traveler. Mrs. Smith tells Amex to send her two cards, one with Mr. Smith's name on it.
Mr. Smith, a Gold member, checks in and stays at a Sheraton for a $200 base rate. He earns at least 600 points in his account for the stay. She earns at least 400 points in her account for the spending. He may actually end up with a little more due to other Gold bonuses. She may actually end up with a little more because she'll also earn on any room taxes. So maybe it's 850 and 450.
- Can you book all hotel stays as Mrs. Smith the primary guest with Mr. Smith as the second guest? As a one-off, I have done this successfully: I'm Marriott elite, wife is not, so I make myself Guest 1 and her Guest 2. She checks in no problem. Long-range for business travel, I'm guessing it's not feasible because of either your corporate travel system or your receipt reimbursement process. If you did this, her name would appear on the receipts.