I keep running into problems with the Terminal package from the Elementary OS daily builds repository. I can't seem to install updates from a previous version of Terminal nor reinstall Terminal from scratch with the daily builds repository. If I remove the repository and purge the terminal package, I'm successfully able to install the old version of Terminal, but I'd like to test and try out the latest daily build version to see what progress is being made etc. Perhaps there is a better venue to give feedback on malfunctioning daily build packages?
The packages in the daily PPA for 16.04 are currently not being actively maintained.
Since the daily PPA is for testing development versions of elementary apps, and the current development version of elementary is based on 18.04, not a lot of effort is going into maintaining compatibility with 16.04.
The description of the PPA says it best:
Do NOT install this PPA if you want a tested running system, this PPA contains the newest and most unstable development of elementary, it's useful only if you are a developer and are not afraid to encounter CRITICAL BUGS. Also this PPA may overwrite already installed packages you don't want it to!
The recommended course of action would be to switch to the stable PPA which has tested, working packages for 16.04, or manually install a working version of terminal as suggested in another answer.
It doesn't install nor downgrade, because the package is jacked. Look at the size of it!
Meanwhile, what you can do (as I did) is to manually overwrite all the files from your computer with the ones you extract from an older version that you can download from here. Just be careful to keep the same permissions for the files you're replacing.
Or, install pantheon-terminal ~daily~ubuntu5.0.1 over yours.
Answer to your questions ...
1. The address I gave you leads directly to the file in question, but the source is the same as yours.
2. If I take pantheon-terminal_0.4.3+r1069+pkg51~daily as the newer build for ~ubuntu16.04.1, by old version I mean an older build for ~ubuntu16.04.1.
3. Since I don't use Eddy because the only time I tried it, it didn't warn of or install the missing dependencies (I use the long tried Gdebi) I can't say for sure. As a general rule, it should retain those permissions. My warning was only for what you'll manually copy with your user account over something installed as root.
4. If you don't clean your system too often, you might find an older build for what you have already installed in /var/cache/apt/archives/ or go afresh with another version.