For info on how to take a photo in your app, take a look at the Android Developer documentation. It is detailed and it has a sample project that you can use.
To send emails, you could use the code snippet from this SO Answer, shown below:
Intent i = new Intent(Intent.ACTION_SEND);
i.setType("message/rfc822");
i.putExtra(Intent.EXTRA_EMAIL , new String[]{"recipient@example.com"});
i.putExtra(Intent.EXTRA_SUBJECT, "subject of email");
i.putExtra(Intent.EXTRA_TEXT , "body of email");
try {
startActivity(Intent.createChooser(i, "Send mail..."));
} catch (android.content.ActivityNotFoundException ex) {
Toast.makeText(MyActivity.this, "There are no email clients installed.", Toast.LENGTH_SHORT).show();
}
I hope this helps.