Android - Activity VS Fragmentactivity

Difference between Activity and FragmentActivity

A FragmentActivity is a subclass of Activity that was built for the Android Support Package.

The FragmentActivity class adds a couple new methods to ensure compatibility with older versions of Android, but other than that, there really isn't much of a difference between the two. Just make sure you change all calls to getLoaderManager() and getFragmentManager() to getSupportLoaderManager() and getSupportFragmentManager() respectively.

Activity, AppCompatActivity, FragmentActivity, and ActionBarActivity: When to Use Which?

I thought Activity was deprecated

No.

So for API Level 22 (with a minimum support for API Level 15 or 16), what exactly should I use both to host the components, and for the components themselves? Are there uses for all of these, or should I be using one or two almost exclusively?

Activity is the baseline. Every activity inherits from Activity, directly or indirectly.

FragmentActivity is for use with the backport of fragments found in the support-v4 and support-v13 libraries. The native implementation of fragments was added in API Level 11, which is lower than your proposed minSdkVersion values. The only reason why you would need to consider FragmentActivity specifically is if you want to use nested fragments (a fragment holding another fragment), as that was not supported in native fragments until API Level 17.

AppCompatActivity is from the appcompat-v7 library. Principally, this offers a backport of the action bar. Since the native action bar was added in API Level 11, you do not need AppCompatActivity for that. However, current versions of appcompat-v7 also add a limited backport of the Material Design aesthetic, in terms of the action bar and various widgets. There are pros and cons of using appcompat-v7, well beyond the scope of this specific Stack Overflow answer.

ActionBarActivity is the old name of the base activity from appcompat-v7. For various reasons, they wanted to change the name. Unless some third-party library you are using insists upon an ActionBarActivity, you should prefer AppCompatActivity over ActionBarActivity.

So, given your minSdkVersion in the 15-16 range:

If you want the backported Material Design look, use AppCompatActivity
If not, but you want nested fragments, use FragmentActivity
If not, use Activity

Just adding from comment as note: AppCompatActivity extends FragmentActivity, so anyone who needs to use features of FragmentActivity can use AppCompatActivity.

Android - Activity vs FragmentActivity?

ianhanniballake is right. You can get all the functionality of Activity from FragmentActivity. In fact, FragmentActivity has more functionality.

Using FragmentActivity you can easily build tab and swap format. For each tab you can use different Fragment (Fragments are reusable). So for any FragmentActivity you can reuse the same Fragment.

Still you can use Activity for single pages like list down something and edit element of the list in next page.

Also remember to use Activity if you are using android.app.Fragment; use FragmentActivity if you are using android.support.v4.app.Fragment. Never attach a android.support.v4.app.Fragment to an android.app.Activity, as this will cause an exception to be thrown.

What are the differences between activity and fragment?

Those are two completely different things:

An Activity is an application component that provides a screen, with which users can interact in order to do something. More details:
https://developer.android.com/guide/components/activities/intro-activities

Whereas a Fragment represents a behavior or a portion of user interface in an Activity.
https://developer.android.com/guide/fragments

What is the difference between Fragment and FragmentActivity?

A Fragment is a section of an Activity, which has:

its own lifecycle
receives its own input events
can be added or removed while the Activity is running.

A Fragment must always be embedded in an Activity.

Fragments are not part of the API prior to HoneyComb (3.0). If you want to use Fragments in an app targeting a platform version prior to HoneyComb, you need to add the Support Package to your project and use the FragmentActivity to hold your Fragments. The FragmentActivity class has an API for dealing with Fragments, whereas the Activity class, prior to HoneyComb, doesn't.

If your project is targeting HoneyComb or newer only, you should use Activity and not FragmentActivity to hold your Fragments.

Some details:

Use android.app.Fragment with Activity. Use android.support.v4.app.Fragment with FragmentActivity. Don't add the support package Fragment to an Activity as it will cause an Exception to be thrown.

A thing to be careful with: FragmentManager and LoaderManager have separate support versions for FragmentActivity:

If you are using a Fragment in an Activity (HoneyComb and up), call

getFragmentManager() to get android.app.FragmentManager
getLoaderManager() to get android.app.LoaderManager

if you are using a Fragment in a FragmentActivity (pre-HoneyComb), call:

getSupportFragmentManager() to get android.support.v4.app.FragmentManager.
getSupportLoaderManager() to get android.support.v4.app.LoaderManager

so, don't do

//don't do this
myFragmentActivity.getLoaderManager(); 
//instead do this:
myFragmentActivity.getSupportLoaderManager();

//don't do this:
android.app.FragmentManager fm = myFragmentActivity.getSupportFragmentManager();
//instead do this:
android.support.v4.app.FragmentManager fm = myFragmentActivity.getSupportFragmentManager()

Also useful to know is that while a fragment has to be embedded in an Activity it doesn't have to be part of the Activity layout. It can be used as an invisible worker for the activity, with no UI of its own.

Fragment vs. FragmentActivity

FragmentActivity is our classic Activity with fragment support, nothing more. Therefore FragmentActivity is needed, when a Fragment will be attached to Activity.

Well Fragment is good component that copy the basic behaviors of Activity, still not a stand-alone application component like Activity and needs to be attached to Activity in order to work.

Read here Difference between Fragment And FragmentActivity

Why fragments, and when to use fragments instead of activities?

#1 & #2 what are the purposes of using a fragment & what are the
advantages and disadvantages of using fragments compared to using
activities/views/layouts?

Fragments are Android's solution to creating reusable user interfaces. You can achieve some of the same things using activities and layouts (for example by using includes). However; fragments are wired in to the Android API, from HoneyComb, and up. Let me elaborate;

The ActionBar. If you want tabs up there to navigate your app, you quickly see that ActionBar.TabListener interface gives you a FragmentTransaction as an input argument to the onTabSelected method. You could probably ignore this, and do something else and clever, but you'd be working against the API, not with it.
The FragmentManager handles «back» for you in a very clever way. Back does not mean back to the last activity, like for regular activities. It means back to the previous fragment state.
You can use the cool ViewPager with a FragmentPagerAdapter to create swipe interfaces. The FragmentPagerAdapter code is much cleaner than a regular adapter, and it controls instantiations of the individual fragments.
Your life will be a lot easier if you use Fragments when you try to create applications for both phones and tablets. Since the fragments are so tied in with the Honeycomb+ APIs, you will want to use them on phones as well to reuse code. That's where the compatibility library comes in handy.
You even could and should use fragments for apps meant for phones only. If you have portability in mind. I use ActionBarSherlock and the compatibility libraries to create "ICS looking" apps, that look the same all the way back to version 1.6. You get the latest features like the ActionBar, with tabs, overflow, split action bar, viewpager etc.

Bonus 2

The best way to communicate between fragments are intents. When you press something in a Fragment you would typically call StartActivity() with data on it. The intent is passed on to all fragments of the activity you launch.