How safe Skype is on rooted Android OS? Recently I have rooted my Android phone to third party custom ROM. After rooting, I have gone through many articles which says rooting cause serious security issues. 

Now my question is: how safe is my Skype? Can anyone access my Skype account? Can anyone record the video conversation of mine? The provider of custom ROM has any hold or control over my phone?
The provider of all the rooting software you use (such as Kingroot if you use a "one-click" technique, SuperSU, and any software you give root permission on your phone), and the provider of the ROM you use (whether it's a custom ROM or the stock ROM) has complete control over your phone. They can steal any passwords you type into the phone (in apps, websites, or your Google account details). They can take control of any app, including Skype. They can record all your conversations, steal your credit card number, and use your details to masquerade as you. They can lock your phone (as well as any online accounts you logged into) and demand a payment from you to get your files and accounts back.

When you decide to root your phone, you need to have complete trust in all the software you use to do it, which means you also need to trust the person you got it from (e.g. the website you downloaded it from). When an app on your phone asks for root permissions, you need to have complete trust in the source of the app. If you don't have complete trust, don't root your phone/install the custom ROM/install the app.