I have so far tried to export my private keys and import them via Coinomi but I am starting to get errors on there.
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3) Tried coinomi to transfer ZEC (only 2/4 worked, connection errors now..)
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Did you try to reinstall coinomi?
It sounds strange that you get connection errors after already successfully transfering 2 out of 4 wallets out.
What other wallets did you try?
Regarding your connection issue:
Did you try the mobile wallets with your wifi connection or mobile connection?