I want to disable or delete stock web browser because I don't use it. Can it cause problems? For example, if its used as embedded rendering engine in other apps (like IE is used in Windows apps), they'll fail to load web pages.
Applications use a Webview to display web content. But it's not dependent on the standard browser.apk rather the browser uses the same webview as all other apps.
If your apps are well behaved than no it doesn't cause any problems. If they aren't than instead of calling a general INTENT to launch a web browser they could call the built-in browser.