I will attempt to answer your questions from a German point of view.
Missing out on the best way to store such an amount of money for a long time
Your bank account is safe
You could "store" an amount of EUR 10,000 in your usual bank account. In Germany, a deposit insurance (Einlagensicherung) with up to EUR 100,000 coverage comes with your bank account automatically, so you won't lose your money in case the bank goes bankrupt.
Setting up an emergency fund
First, as you don't have any debt yourself, set aside some money for an emergency fund, if you don't have one already. Your bank account (or Tagesgeldkonto) is a good choice, because the money is available right away if needed. Ideally, you would then be able to pay your bills for at least 3 months without any income.
This makes sense, as in Germany, it can happen that you will receive unemployment benefits (Arbeitslosengeld I) no earlier than 12 weeks after you lost a job -- for example, if for some reason you were forced to quit a job instead of your employer terminating your contract (Sperrzeit, see § 159 SGB III).
Also, if the company you're working for would go bankrupt, you're entitled to receive Insolvenzgeld (insurance for employees by the Federal Employment Agency in case of employer bankruptcy). But again, this will happen only if your employer couldn't pay your salary for at least 3 months in a row.
Invest with long-term perspective
Depending on your living standard (your monthly expense budget), you will still have a good portion of the EUR 10,000 left after setting up your emergency fund. However, simply "storing" the money for a "long time" is probably not quite what you want: Due to inflation, the value of your money will decrease over time.
If you don't need the money for a long time (at least 10-15 years or more), your best bet would be to invest in a really widespread ETF (ideally worldwide). This way, you mitigate your risk if the economy in certain sectors or regions goes down.
Nowadays, many Germany direct banks (for example DKB, Comdirect or ING) offer a brokerage account basically for free, you would only pay for transaction fees. As ETFs are automated, the management fees are comparably low, also.
Losing money to bureaucracy (German authorities)
Situations to consider regarding authorities
Indeed, you should take German authorities into account. Should you ever get yourself into a financially difficult situation, the government will expect you to pay out of your pocket first, before they pay any money to you.
If you are unemployed for a longer time (more than 12 months), you will no longer receive the usual unemployment benefits (Arbeitslosengeld I), but rather Arbeitslosengeld II ("Hartz IV"). If this happens, the government will expect you to use up your own savings before they give any money to you.
You will be allowed to keep a certain amount depending on your age, called Schonvermögen. It is roughly EUR 150 multiplied by your age. There are various online tools to calculate the exact amount, and there is currently a maximum of EUR 9,750.
A very similar situation happens if your girlfriend is unemployed for a longer time. If you're living in the same household together, the authorities will assume that you share a certain responsibility for each other, called Bedarfsgemeinschaft.
In this case, your girlfriend's savings and your savings will both count together (see link above). This means, your girlfriend won't receive any benefits as long as you don't use up enough of your savings. So you might be forced to pay for your girlfriend's living expenses indirectly.
Authorities might also force you to use up some of your savings if you do not earn enough money, for example if you will have a child and need to pay child support. If your regular income is low, but you have a lot of money in the bank, you might need to use that money.
However, in such a case, regulations are rather vague. The exact outcome will depend on the individual situation. There is no simple calculator for such situations. Should you ever be in that situation, a family court would have the final say.
In any case, it is better to have some money in the bank and use it in case of a financial emergency -- rather than having no savings at all -- because you might not receive social benefits immediately.
As as side note, there is no way to simply transfer your money to another person (for example, back to your father) to "protect" it from the government. If you apply for social benefits, they will ask you specifically if you gave away large amounts of money in the past.
Losing money on the transaction due to some taxes (I have no idea about this)
Taxes that could play a role
This is called Schenkungssteuer ("gift tax") in Germany. It depends on the relationship between the donor and yourself. If your father is giving money to you (his child), there is a tax-free amount of EUR 400,000 (see § 16 ErbStG), so tax won't be an issue if this is a one-time transaction.
The EUR 400,000 tax-free amount is for a time span of 10 years - ten, instead the usual one year for tax-free amounts. And it is not about gifts from your father, but about the sum of gifts given to you, as you would pay tax for the money that exceeds the limit. So for EUR 500,000 in 10 years, you would pay tax on EUR 100,000 in the year it exceeds the limit.
If you choose to invest (part of) the money as suggested above, you would have to pay capital gains tax. But again, there is a tax-free amount per year called Sparer-Pauschbetrag. Make sure to set up a proper Freistellungsauftrag at your bank, so they won't accidentally deduct taxes.
