yes>> Can I run normally on wifi
no>> or do I need proxies?
Depends, generally if you have more than 3-5 accounts, yes you should.should I use proxies?
Do you want to hide from twitter you are controlling this account? Then yes you should use proxies
yes>> Or is it possible to run on VPN?
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Let me try and explain better

Proxies allow you to hide the IP of who is controlling the account. You can use proxies in your browser, you can use them in the app. If you normally connect to your twitter account manually through your browser with a proxy, then you may want to use a proxy in the app, but if you don't use a proxy manually, then you do not need to use one in the app. If you log into your account(s) with your local IP, do the same with the app. There is nothing to hide.
But, if you want to control 100 accounts, then you cannot do this from a single IP, so you do need to hide, one person is controlling 100 accounts, so you would need proxies.
As for a VPN, a VPN just changes the base IP of the machine you are using. Every app on the machine will automatically route through the VPN IP, it's a low level network protocol, that applications are not aware of, they use it without knowledge automatically. Proxies are in the application layer network protocol, meaning applications are proxy aware and can choose which network HTTP request is routed through which proxy.
If that doesn't make sense, just go with the yes/no/yes answers above

Regards,
Martin
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