For the moment, nothing much would happen. EU law does allow member states to deny residency to EU citizens who don't have work or sufficient financial resources and ban them from receiving aid from the state, but unlike a few other EU countries, Germany has not used those provisions aggressively until now.
As far as I know, you can still register without proving you have resources or showing a work contract and once you are registered, you can live there without any problem. In fact, you could even apply for some types of welfare benefits, which is one of the reasons why it became such a hot topic politically. Despite all the talk, I am not sure if anything has changed yet and it's difficult to know exactly what will happen in the next few months.
But it's possible to take some cues from EU law and the practice in other EU countries to have some idea of what's possible or not. Even in countries that already expel jobless EU citizens (or ask them to leave), you can often fly under the radar. The authorities do not necessarily actively seek each and every jobless foreigner. Mostly, it's about avoiding to pay welfare benefits, making sure poor migrants from Romania and Bulgaria do not become permanent residents and showing that “something is being done”. So if you don't attract attention (e.g. by applying for financial support from the state), they might just as well let you be.
Also, three months is the threshold to differentiate visits from residency but in principle, you can at least look for work for at least another three months (so six months in total). It's only after that time that you could possibly be asked to leave.
Importantly, working is not the only way to qualify for the EU treaties' freedom of movement. You can also do it as a non-economically active person. The main condition is having sufficient resources to avoid being a burden to the social safety net. So if your girlfriend can find a few thousand euros to put on her bank account and has health insurance, she will in any case be able to reside in Germany completely officially.
Now, regarding your second question, if she finds a job and then becomes jobless, there are a few subtle rules depending on how long she worked, what type of contract she had, whether she stopped working because of an illness or accident but she can certainly stay and look for work for another six months, possibly more.
Also, if she worked more than five years in the country, she automatically becomes a permanent resident. She can then stay indefinitely, collect welfare benefits, etc. just like German citizens and it will be virtually impossible to force her to leave. The same obviously applies to you, incidentally.
Finally, regarding your third question, being married changes everything. If you work in another EU country, your wife has an unconditional right to stay with you (and vice versa). Only one of you needs to qualify to be a resident according to the rules I detailed above. If you are yourself in the country legally, she cannot be expelled, be asked to justify her resources or anything like that. In many cases, some form of registered partnership other than marriage works too.
This answer on another Stack Exchange site details the legal basis for all this.