This is Svante, Lead Developer at AxCrypt - i.e. the author of both version 1 and version 2. Obviously I'm biased, but I also do know exactly what we do with your information.
1a) We require an e-mail address - but so does just about any Internet-based service on the planet. Your e-mail should not be considered a secret, because it's not. There is no way (without the password) to know the e-mail address of the person who encrypted a particular file, or who it is shared with. The main guiding principle behind AxCrypt 1 & 2 is that nothing is assumed to be secret, except your password. Not the source code, not the algorithms. We even assume an attacker has extensive access to both encrypted text and the original plaintext. What we store on the server, which relates to the password, is a small number of files encrypted with your password. The point being - we're already assuming an attacker has access to files encrypted with your password. A leak of stored data from the server does not change that assumption.
1b) We do have your password transiently on the server though, when we decrypt above-mentioned files, and it also travels over the internet encrypted with SSL. That's another assumption - that current standards for Internet-encryption such as SSL can be trusted. Yes, we do trust that. Also, mounting a successful attack against a specific server running SSL, even if there are flaws, require quite extensive resources typically requiring at least at the level of a national agency. We are based in Sweden, our source code is written in Sweden, or servers are running in Sweden. We would not be affected by a for example directives concerning requirements of key disclosures or backdoors made by government agencies in a large english-speaking union of states west of the atlantic ocean.
2) Is it safe? In the end, that's a judgement call. There is no such thing as proven safe, only proven unsafe. What we try to do is to give full disclosure on what we do and what the assumptions are. We are open source, and with among the longest track records of *any* file encryption software. Personally, I trust AxCrypt. I use it. I might be wrong, but I have a fairly good insight into the tradeoffs made.
3) AESCrypt can certainly be an alternative, but it has less functionality than AxCrypt 1.x. Specifically it has no provision for automatic re-encryption, no secure delete. AxCrypt 2 has even more functionality and is much easier to use, and to share encrypted files with others should you wish to. AESCrypt is available on several platforms. We're working on fixing that for AxCrypt.
BTW, AxCrypt 2 is entirely devoid of any adware such as OpenCandy. It is an entirely clean download and install. Instead we added features on top of AxCrypt 1 that are available with the AxCrypt premium subscription.
Also, some people have made the assumption that because there is a commercial subscription, AxCrypt 2 is no longer open source. It still is. Get the source at https://bitbucket.org/axantum/axcrypt-net .