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German tax issues are very complicated, so you are well advised to ask a professional tax consultant for definitive answers. (You will need one anyway fo your yearlöy tax declaration!)
As far as I know, you can only get benefits for your family members (Kindergeld, tax class, etc.) if they are living with you in Germany.
Support sent to family members is only tax-deductible if they are poor and if the payments are mandated by law.

As far as I know, you are in principle entitled to receive Kindergeld. The level of Kindergeld for children living in other EU countries of parents working in Germany has been a matter of much political debate, in particular for countries such as Romania were the cost of living is much lower and the German Kindergeld is very high by local standards. Austria has enacted a law to adapt Kindergeld to the local level of where the children live. But this law is being challenged by the EU.

I do not know if you are entitled to Kindergeld *from the first day* you work in Germany.

I don't think you can send money tax free to your home country. You can deduct "außergewöhnliche Belastungen", exceptionally high expenses, e.g. for cost of surgery if your insurance doesn't cover it and the like. But this is the same for locals.

Generally, "thanks to the EU", EU members are treated pretty much the same as locals.

As far as I know, Kindergeld is only given for kids living together with you. But please check that with an expert or the relevant authority.

"Kindergeld  wird  für  Kinder  –  unabhängig  von  ihrer  Staatsangehörigkeit  –  gezahlt,  wenn  sie  in  Deutschland  ihren  Wohnsitz  oder  gewöhnlichen  Aufenthalt  haben.  Dasselbe  gilt,  wenn  die  Kinder  in  einem Mitgliedstaat der Europäischen Union oder des Europäischen Wirtschaftsraumes oder in der Schweiz leben."

Google Translate: "L'assegno familiare viene pagato per i bambini, indipendentemente dalla loro nazionalità, se vivono o lavorano in Germania avere residenza abituale Lo stesso vale se i bambini di
uno Stato membro dell'Unione europea o dell'Unione europea
Area economica o vivere in Svizzera."

Source:

You can apply for Kindergeld here:
If you don't read and write German, you may want to ask a German colleague or your employer for help.

Enjoy.

Thanks very much for your help. I'll definitely ask for help to an advisor. However, As fa as I am informed, I can only apply for "kinderkeld" if I have first registered my son in Germany (anmeldung) then he can go living wherever in the EU.