Is it reasonable to fight the deportation note to buy time? During this time, she could get the certificate for A1 language, and I could prepare all documents and even find work. However, I'm afraid that we need to wait for the outcome of the case before she is free to go? And of course there's the possibility that the court ruling is not in her favor and then deportation takes place anyway.
If possible, an appeal is definitely reasonable in those circumstances. That's less critical if you don't intend to live in Croatia later on but immigration infringements of any kind can have a negative impact years down the line so it's always better to do everything you legally can to keep a clean record.
It's difficult to see how such an appeal would curtail her right to leave the country. Unless she is already in detention and as long as she has her passport, your girlfriend will always be free to go. The worse that can happen is that she would be deemed to have abandoned the procedure, that the ban is reinstated, or that the whole time since her permit expired now counts as overstay. And obviously, whatever tolerance Croatia may extend during the procedure does not apply to the rest of the EU (which is why you may have read that she is not “allowed” to leave the country) but that doesn't mean she is barred from, e.g., going back to the Philippines.
I may be wrong about that as I do not know Croatian practices but in general, immediate detention and removal to the Philippines at the end of the procedure also seem unlikely. In the EU countries I know, she would probably get another notification and the opportunity to leave freely (that's much cheaper than a removal and resources are limited). EU law also favors “voluntary” departure at every step of the way, some countries even offer financial incentives (I don't remember all the details off the top but that's what the “Return” directive, directive 2008/115/EC is about). From the perspective of the Croatian authorities, her leaving (especially to the Philippines but also to another country that would take her) is a win, they are not trying to force her to stay in the country any day longer than necessary.
Is it more reasonable to go back to Philippines and wait until her Schengen ban is lifted? During that time we could prepare everything for her entry to Austria. But it would be far away and it's more difficult to support her there, financially as well as mentally. Also, she's worried about sexual harassment because she was already facing severe issues in her country.
Or is it more reasonable to go to a 3rd country (ie. Serbia) and wait until her Schengen ban is lifted?
Or is it more reasonable to go to a 3rd country (ie. Serbia) and wait until her Schengen ban is lifted?
Either of these are reasonable but ultimately the ban may not matter as much as you think. The first order of business is working with a lawyer to find out what she needs to reside in Austria and how to get there. An entry ban is not necessarily a dealbreaker (family life trumps minor immigration infringements), it really depends on Austrian law. In other countries, even irregular stay or entry do not always preclude getting a family residence permits. I do not advocate doing this lightly as it certainly can have very negative consequences but it's important to realize short visits and family reunion are two very different situations legally speaking.
Conversely, if for some reason Austrian law doesn't recognize your relationship or there is some other administrative hiccups, the fact that the ban ended won't be the end of your troubles. While entry in the Schengen area won't be automatically refused, it might remain very difficult for years to come. Consular officers and border guards will have several ways to notice her past overstay and they can still take that into account when determining whether your girlfriend fulfills the requirements for entry.
You should also consider the possibility that she might be refused entry in a third country like Serbia or Turkey (e.g. based on her lack of valid visa or permit for her current stay in Croatia). As a Filipino citizen, the Philippines is the only country she has an iron-clad right to enter. I have no idea how likely that is but the absolute worse case scenario when trying to enter another country is ending up in detention while the local authorities secure permission to return her to the Philippines. Being “bounced” at the land border with Serbia could also prompt Croatian detention and execution of the pending removal order (if that's what you received). There is also the question of what would happen if the appeal in Croatia or procedure in Austria take longer than 90 days (or whatever duration of stay she is granted in that third country).
So while staying in a third country could be a good way to reduce the stress of the current situation, you should primarily focus on securing some stable status in Austria. You might also consider approaching migrant support non-profits in Austria or Croatia, they should be able to advise on the risk of detention and removal and how to avoid it.
If you do marry, one option to consider is moving together to another EU country (or even moving yourself to Croatia). This may seem outlandish and obviously comes with many challenges (finding a job, accommodation, distance from your friends and family, etc.) but I am throwing it out there because that's a way to go around restrictive Austrian regulations. For example, there are no language requirements for the spouse of EU citizens. After some time, you would even be allowed to go back to Austria under these more favorable EU rules (that used to be called the Surinder Singh route in the UK).