What are the current limits on capital inflows and outflows for
individuals and investors? How much currency can be converted
from/into local currency without government approval? Can foreigners
open local bank accounts? Is there any way for a US investor to
convert US dollars to yuan, invest it in an interest-bearing deposit,
and have the ability to convert it back to US dollars at any time?

The current limits on capital inflows and ouflows for individuals are RMB 6,000.
Sum under $ 10,000 can be converted from/into local currency without
government approval.
Sum between $10,000 to $50,000 needs to be registered by local bank.
You can set up a investment firm in China, and then, with the business
licence you can open accounts in local banks.

The question you are asking can be answered in a few parts:

1) Can foreigners open local bank accounts?
Ans: Yes - just bring your passport

2) Is there any way for a US investor to convert US dollars to yuan,
invest it in an interest-bearing deposit, and have the ability to
convert it back to US dollars at any time?
Ans: Yes there is but it is complicated - would take too long to
explain. Suffice to say that money paid into the company as paid up
capital will not be allowed out of the country as dividends. Meaning
that legally, only your profits would be able to leave China.

3) What are the current limits on capital inflows and outflows for
individuals and investors?
Ans: Depends. If you are a foreign national - individual (i.e. non
Chinese citizen), you are allowed to wire in at most US$2.5k a day
into your bank account in China, but not exceeding US$50k a month. As
for outflow, if you wired money in and did not change it into RMB then
you can wire it out again. If not, you have to go through the official
channels (i.e. have the required approvals and have paid all the
relevant taxes etc etc).

4) How much currency can be converted from/into local currency without
government approval?
Ans: Does not matter - all you do is go to another branch or another bank!