How to put the widget to rate nodes in a view next to title?
Since you're using the Rate module, you should configure Views as shown in this image:



So what you need to do, is to configure the field "Votes:Value". As you can see in my image above, within the Appearance Dropdown I selected Rate Widget (compact). if you only have "Rate Widget option or Default" (as in your comment, it's probably because you have not yet added the required Relationships to your view.

Relationships is a way to join tables from another module. To get you going with this also, have a look at the next image:



Some more details about the 3 (numbered) annotations I added in this image:


That's where you add the Relationship, in this case you need to select Content:Votes.
After you added that relationship, within Fields you can now add a new field Votes:Value (that is: because of the relationship that was added, you'll be able to select this specific field from the list of available fields when you try to add an extra field).
After you completed the previous step, automagically in the preview area you'll see a preview of the views results you'll get (don't bother too much about the theming of that preview at this time, what counts is that the result is correct).