Will the current wallet build and run on ARM based hardware?
ARM is not a supported configuration. It might work, it might not. As far as I know, none of us and no community member has attempted an ARM build; you'd be the first person to try.
And if so can I run it on the new Pi Model A+:
There is far too little RAM for the current client. As bytemaster said, we're planning some lighter tools but they aren't ready to go right now. When the tooling is in place, I plan on testing Raspberry Pi based cold storage.
If the Pi A+ is not up to the job (256MB of RAM) then what spec do I need to be looking for?
I'm not sure if we have an official recommendation for amount of RAM, but we know that 2 GB seems to be too low. You might be able to run the CLI wallet only with 4 GB, but 8 GB or more would be better.
I'm really keen to run my wallet on ARM based hardware.
Before buying hardware, you might want to look into qemu-arm-static which will allow you to chroot into an ARM-based Linux environment on x86. If you can get the client to compile and run on an emulated ARM machine, odds are good it will work on real hardware.
The reason I want two machines is that I'd like to have one that I carry with me when traveling etc and one that I have permanently at home for easy access if the other one is lost.
What you really want is to back up your wallet onto a flash drive.
Obviously I password protect my wallet at the moment (in fact I think it's required with the new BitShares client). I'd like to password protect my two new wallets with exactly the same password. But I'm unsure for certain how the passwords work - I'm guessing the password does not live on the blockchain. Can anyone confirm? So if I lost one of my new A+ Pi wallets (assuming they can be used) am I right in thinking that if I changed the password on the one I didn't loose then the lost wallet would still retain the old password? I guess what I'm getting at is that a lost wallet cannot have it's password remotely changed via the blockchain. The password is local and stored with the instance of the wallet correct?
Any clarity someone can shine on my lack of understanding here would be most helpful.
The password is not stored anywhere, rather it is used to encrypt the wallet on the local hard drive. There is no way to change the password remotely; the only way to change it is to use the client to decrypt your wallet with the old password and re-encrypt it with a new password.
On the bright side, if someone steals your traveling computer with your wallet file, it is useless unless they also know or can guess your password. If this happens, I'd recommend creating a new TITAN account with a new client data directory, then transferring all your funds from the old account to the new account. That way, if the thief eventually guesses your password, the old private keys will be useless since they no longer control any funds.
I'd recommend doing frequent wallet backups to multiple removable media devices which you keep in multiple geographic locations until we have better tools for cold storage and lightweight clients.