yes actually. you can sell any amount of BTC instantly on an exchange and wire the money directly to your traditional bank account. the order books generally have the depth to handle selling millions of USD worth of BTC per day without much price impact. if you wanted to sell more many of the exchanges will facilitate an Over The Counter sale that does not effect exchange price.
Yes but not without giving them a few days warning.
Typically the most you can get out of a major branch of a national chain on a moments notice would be $100,000 max. This changes a lot at the regional level and based on the individual bank and the amount of risk they have from robberies.
My credit union couldn't even let us withdraw $20,000 in cash when my business needed it.