Several things
"In California, if I purchase a property at a tax lien auction.. how long do I have to wait for the original owner to be able to redeem it?"
Technically, the owner's right of redemption ends at the tax sale. However, they have a year to challenge the validity of the sale. Once in a while the Tax Collector sells the wrong parcel or does not properly post payment, give notice to the delinquent owner, etc. The former owner can't just show up and redeem after the sale.
see
http://www.co.san-joaquin.ca.us/Treasurer/AuctionPacket04.htm
"Or to phrase it another way.. how soon can I take full title to it in order to resell it?"
You will have title when you pay for it and the Tax Collector issues a tax deed, usually within two months.
"Also, in the meanwhile, can I rent the home out? "
Ummm. You haven't been to a tax sale before have you? It's pretty rare for homes in good condition to be there. Typically it's raw land, a few abandoned industrial sites, some farmland. A home in good condition is rare.
"I've heard that if I do any improvements and the owner later redeems the property, I'm out of luck on the improvements and can only expect my payment plus some interest back in return."
I'm not sure that you would even get interest. I think you only get your purchase price back. Remember that after the tax sale it's not a straight redemption: the former owner has a right to contest the sale, and that right expires in one year. You also have to watch out for lienholders, and heirs if the owner was deceased.
From the link above "The former assessee or any lien holder has one year from the date of recording of the tax deed to challenge the validity of the tax sale (Revenue and Taxation Code 177 and 3725). During this one-year challenge period, it may not be possible to obtain a guaranty of clear title from a title company. Title companies may not issue their policy of title insurance on property that was purchased through tax-defaulted public auction, unless a quiet title action has been successfully pursued in the courts, or in lieu thereof, quit claim deeds are acquired from the former assessee or every lien holder. To learn more about quiet title actions, you may consult with an attorney experienced in real estate transactions."
