Signatures not appearing

I am guessing you are confused by the new signature system in phpBB 3.x, check
User Control Panel - Board Preferences - Edit Display Options - Display Signatures

I haven't done anything about feeding profile data back to Drupal because phpBBs new profile system is much more complex than what you can easily do in Drupal. It's doable for sure, the 4.7 module shows you have to transfer from Drupal's custom profiles to phpBB, which is the same idea but in the opposite direction.

Signatures appear to work, but you have to check them off on each post (I personally think signatures are a waste of space when the name is to the left anyway, but you can change this)
http://kepp.net/drupal-5.1/forum/viewtopic.php?p=101#101

I haven't heard about any complaints regarding signatures. If you are still having trouble I suggest you try changing your users signature in Drupal and watch the corresponding user in phpBBs database using something like phpMyAdmin. If it doesnt change, but it shows up in Drupals user profile, then the module is not doing its job. Otherwise you have a phpBB problem.

{L_VIEWING_PROFILE} is an artifact of phpBBs template system, it's not a variable you can access from anywhere else.

You should probably write a small, new module that implements hook_user in Drupal and displays the fields you want. Figure out how this "L_VIEWING_PROFILE" is stored in phpBBs database and get it straight from there.

custom profiles is not designed to reach out to other databases, I am not aware of any modules that do this, but I would not be surprised if they exist. If it's a commercial undertaking you can hire me or someone else to do it, probably not hard.

If you want signatures on by default do this:
Open the .module file, find line 80, replace

$query = "INSERT INTO " . $prefix ."users (`user_id`,`username`,`user_password`,`user_regdate`,`user_email`,`user_timezone`) "
					." VALUES(" . $edit['uid'] . ",'" . _phpbb_encode($edit['name']) . "','".md5(_phpbb_encode($edit['pass']))."'," . time() . ",'" . $edit['mail'] . "',1.0)";

with

$query = "INSERT INTO " . $prefix ."users (`user_id`,`username`,`user_password`,`user_regdate`,`user_email`,`user_timezone`,`user_attachsig`) "
					." VALUES(" . $edit['uid'] . ",'" . _phpbb_encode($edit['name']) . "','".md5(_phpbb_encode($edit['pass']))."'," . time() . ",'" . $edit['mail'] . "',1.0,1)";

(Notice the "user_attachsig" on the first line and the additional "1" in the end. Make these changes yourself, do not cut'n'paste from this page because Drupal sometimes messes up code)

I should add, you can, as the phpBB admin, edit any existing user profiles to enable signatures by default.