1. When a Modal is opened,set focus on a predefined <input> inside this Modal.

Define a directive and have it $watch a property/trigger so it knows when to focus the element:

Name: <input type="text" focus-me="shouldBeOpen">

app.directive('focusMe',function($timeout,$parse) {
  return {
    //scope: true,// optionally create a child scope
    link: function(scope,element,attrs) {
      var model = $parse(attrs.focusMe);
      scope.$watch(model,function(value) {
        console.log('value=',value);
        if(value === true) { 
          $timeout(function() {
            element[0].focus(); 
          });
        }
      });
      // to address @blesh's comment,set attribute value to 'false'
      // on blur event:
      element.bind('blur',function() {
         console.log('blur');
         scope.$apply(model.assign(scope,false));
      });
    }
  };
});

Plunker

The $timeout seems to be needed to give the modal time to render.

'2.' Everytime <input> becomes visible (e.g. by clicking some button),set focus on it.

Create a directive essentially like the one above. Watch some scope property,and when it becomes true (set it in your ng-click handler),executeelement[0].focus(). Depending on your use case,you may or may not need a $timeout for this one:

<button class="btn" ng-click="showForm=true; focusInput=true">show form and
 focus input</button>
<div ng-show="showForm">
  <input type="text" ng-model="myInput" focus-me="focusInput"> {{ myInput }}
  <button class="btn" ng-click="showForm=false">hide form</button>
</div>

 Plunker
 
      
 
      
 Update 7/2013: I've seen a few people use my original isolate scope directives and then have problems with embedded input fields (i.e.,an input field in the modal). A directive with no new scope (or possibly a new child scope) should alleviate some of the pain. So above I updated the answer to not use isolate scopes. Below is the original answer:
 
      
 Original answer for 1.,using an isolate scope:
 
      
Name: <input type="text" focus-me="{{shouldBeOpen}}">
 
      
 
 
      
 
      
 Plunker.
 
      
 Original answer for 2.,238)"><button class="btn" ng-click="showForm=true; focusInput=true">show form and
 focus input</button>
<div ng-show="showForm">
  <input type="text" focus-me="focusInput">
  <button class="btn" ng-click="showForm=false">hide form</button>
</div>
 
      
 
 
      
 Plunker.
 
      
 Since we need to reset the trigger/focusInput property in the directive,'=' is used for two-way databinding. In the first directive,'@' was sufficient. Also note that when using '@' we compare the trigger value to "true" since @ always results in a string.