Hey Kaan,
The email authentication for old versions will continue to work for a short time, so you should be able to transition those projects to interface with OAuth using the --oauth2 flag and the appcfg oauth2 credentials generated by going through the oauth2 flow once with either an old or new SDK.
As to your patched SDK, if you have patches to make to the SDK, and you rely on services that SDK interfaces with, you should submit patch requests to the public issue tracker so that you don't end up having to maintain what amounts to a fork which still has the responsibility of keeping up with developments to the underlying service.
If your old patched SDK is only needed for development and you don't wish to submit the patches for "shortcomings and various bugs", then you could of course, as you say, use the new SDK to deploy and use the old patched one to develop. Be aware that this cuts you off from future development server releases unless you do the hard work of merging the fork back into the main branch developed by Google in future releases.
I can't comment authoritatively on the reason for removing password authentication but if I were to make an informed guess it's likely because the security features of having a single authentication flow at a single location (
accounts.google.com login when you go through a login flow) making it preferred over sending passwords through a side channel maintained by App Engine and the SDK. Otherwise the certificates and encryption involved would need to be maintained and upgraded in parallel, etc. This is just one possible line of reasoning, not a comment from a dev involved.
Sincerely,
Nick