Open mic night on interest rate spreads

Ok, readers. Here's a chance for you to flex your muscles. The following chart shows various short-term interest rates:

Why are these rates all so different? Can the differentials between them be arbitraged away? What sorts of institutional rigidities might be preventing arbitrage? For instance, we know certain institutions like Fannie Mae and Freddie Mac can't get interest on reserves held at the Fed. What other sorts of fine details might be important? Or are the differentials between these various rates not currently open to arbitrage? Can they be explained by term risk? How much do other sorts of risk, like liquidity risk, counterparty risk, default risk etc drive spreads? A few specific questions:

a) The DTCC Treasury General Financial Collateral (GCF) repo rate used to trade at or below the fed funds rate. The Treasury GCF repo rate is a collateralized rate. Since collateral reduces risk, it makes sense it would trade below the fed funds rate. But why is the riskier rate now below the safer rate?

b) Why does the Fed funds rate generally trade above the t-bill rate? There's presumably less term risk in the FF rate, which would imply a lower Fed funds rate. Does interbank risk account for the higher fed funds rate?

c) Is it a risk-free trade to fund oneself in the fed funds market and invest the proceeds overnight at the interest rate?

d) Why would banks hold t-bills at all if they can simply keep reserves at the Fed for a superior return of 0.25%? The credit risk seems similiar: as a bank, you're exposed to the Fed in the case of reserves, and the Treasury in the case of bills.

e) Sometimes the 4-week t-bill yield crosses over the 3-month. Why? The credit risk is the same, and presumably bills are equally liquid. Are these inversions purely related to expected changes in yields?

Data, ideas, links,etc all much appreciated. I'm sure I'll have more questions in the comments, or if you have other interesting observations, go for it.

[Update 22/03/2013: I reinputted the Treasury GCF rate since my original data was off]

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