RE: Is there a limit in a day to the number of accounts I can sponsor in Hive SBI? How about sponsoring my wife and second son's accounts? Is this allowed?

Great question !

As far as I know, there's no limit, either daily or in total. The more people contribute to the project, the more HIVE it'll generate to deliver earnings. Plus, for each SBI you buy someone you get a bonus unit of your own. There are people with thousands of SBI's - one day I'll get there ! 

The way it works is that each user's SBI's generate a vote value which gradually increases over time. When they post, some of that vote value is used to create an upvote. The vote value stored is reduced by that amount, and carries on building up. There is a minimum upvote, but once you've got a few SBI's that really isn't an issue unless you're making huge numbers of posts.

It's worth remembering that you're buying SBI's, so it's a permanent transaction, not like a delegation that you can recall when you want. You also need to take a long view; it'll probably take a year or two before the earnings delivered covers the initial cost of the SBI's, but after that it's all pure income.

A good place to look is https://www.hivesbi.com/ - you can see how many units and bonus units you've got, plus estimates for your next vote and total delivered so far.

All in all, I'm a big fan of the SBI project. They are a great way to give rewards to people and give something back to the community; I aim to sponsor about 4 SBI's a week (2 for creative writing in the Worldbuilders community, and from 1 to 3 in the #SaturdaySavers weekly author rewards).