You can get a mate in the trial version, you just have to have 800+ experience. It's the same as in the full version. You do need the full version to progress and have pups though.
For trial, it is best to order something inexpensive that which you have to use like milk or soap. Some apps mention that they deduct a small percentage of payment...
When you say "very first version", I think you mean first playable version. Yes, you can change it to the fist playable versions by clicking on "enable Alpha" or "enable...