After going through Google and trying a lot of workarounds, I found a one that really worked for me.
1. Wifi issue got fixed automatically. I keep the Auto updates on 'On', so all the apps get updated automatically, so I guess one of such update fixed it. I didn't do anything else apart from restarting the phone unconsciously, once in a while.
2. The second one was really a pain for me for the last 3-4 months. But then today I went to Settings --> More --> Default Applications --> Home. I could see 3 options - Touch Wiz Home, Touch Wiz Easy Home and Connect for Hotmail. On the right hand side there is an option to delete each of them, so I deleted 'Connect for Hotmail' and that inturn uninstalled Hotmail from my phone and this issue got fixed

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