I have to agree with the TSA that carrying more than $500 or so in cash is definitely suspicious. Usually a sign of drug trafficking or other illegal smuggling (but most smuggling is in the drug trade), or possibly counterfeiting (although that's unusual).
Nonsense. Carrying a large amount of cash is a sign of nothing other than carrying a large amount of cash. And $500 is peanuts if you're going somewhere where credit and debit cards aren't in much use.
It's not against the law to carry as much cash as you want (except that you need to declare if you're bringing more than $10,000 in cash in or out of the country).
The federal civil asset forfeiture laws were amended in 2000 because they were being abused by law enforcement, and the federal circuit courts have been clawing back on the circumstances under which just carrying cash is probable cause for anything else.
Actually you're not allowed to carry more then 9,999$ on your person. If you get caught your money will be confiscated and you will have to prove that every one of those dollars you obtained in a legitimate manner. I know someone who's uncle was interrogated for coming into a bank with 25k he saved on his own (an older man) and he had to prove he had saved that money from his paychecks.