Is bitcoin cryptographically secure
I guess there is no consensus among researchers and academics on the security of Bitcoin protocol. Thanks to Stack Exchange Network, The following links should help you to answer some of your questions:

1- Bitcoin research at Cryptography StackExchange

2- How secure is the Bitcoin protocol? at Cryptography StackExchange

3- Are there any fundamental security vulnerabilities in Bitcoin? at Bitcoin Stackexchange

Here is a comprehensive list of research publications at Bitcoin wiki that include research and analysis of Bitcoin.