Here is what Mystery Plant looked like a couple of weeks ago. There weren't any white leaves with green outside at that time. Thank you again :)

It looks like you have a hoya carnosa krimson princess. It is a variegated form and is known to revert back to plain form (just green leaves) quickly. The reddish tint on some leaves is normal for this species. You can make two plants out of this one, if you desire. Just simply cut all of the variegated (white/green) parts away, stick them in a cup of perlite, let them root, and you will have a new hoya plant!

Thanks so much for your prompt reply! Do you have advice for care of this plant?

Invest in a liquid or water soluble fertilizer. Use it at 1/4 the strength recommended for house plants (mine says use 1 teaspoon per gallon, so I use 1/4 teaspoon per gallon) and use every time you water. Water only when needed; if you put your finger in the pot, up to the first knuckle and it feels damp, you don't need to water. If it is dry, water.
In the spring and summer, you want to use a bloom boosting fertilizer at 1/2 strength the recommended dose for houseplants, and again only when needed.
Evey once in awhile, you will need to "flush" the pot, to get rid of fertilizer salt buildup. You do this by running the pot under water for about 5 minutes. Starting 2-3 weeks before you flush, don't water the hoya. Also, don't water after flushing until the medium in the pot is dry.
Keep neem oil and rubbing alcohol on hand for mealy bugs (houseplants are susceptible to these nasties).
I have to go to work, so hopefully someone else can fill you in, where I left off! Good luck to you and you are already doing a good job!

Here is a link that might be useful: a bit on hoya care

Yay! This level of detail is exactly what I needed. Thank you very very much!