You don't necessarily have to use the login widget - if a logged out user visits a post/page that is blocked, they will be given a login option at that point as well.
Your overlap sounds like a style (CSS) issue. There is no "one-size-fits-all", so there are several additional stylesheets included in the download. Try using one of those. If none of those work with what you have, you can customize a stylesheet as well. A good place to start would the User Guide section on customizing the forms: http://rocketgeek.com/plugins/wp-members/users-guide/customizing-forms/
The plugin does not block widgets from displaying, but you can easily create a sidebar that displays based on login status. There is a premium article on the support site on how to set this up. If you are looking for something free, the concept is similar to setting up menus based on login status, a free tutorial on that can be found here.
As far as redirection, no - the plugin operates on the concept of moving the user around as little as possible. Redirecting users more than necessary results in confused users and degrades the user experience. The plugin operates by default on posting a login attempt to the page that the user is logging in on. So if they are attempting to read a post that is blocked and login on that post, they will stay on that post.
The plugin does not force you to stay within this construct, however. There are plenty of hooks that allow you to create the user experience that you want to create. If you want all logins to end up on the home page, there is a filter hook for that - wpmem_login_redirect. (A full list of action and filter hooks is available here.)