A white (or sometimes yelllow) mark on the ground (looks like undecipherable letters) indicates someone else's sign, which you can use to summon that person to your world for jolly coop.  Most of them are from real people, but you'll come across some NPCs who can be summoned as well.  If you've beaten the Taurus Demon and gone on just a bit farther, you should find someone to talk to who will give you an item which allows you to do the same thing, i.e. put your own sign down so that someone else can summon you to his world.

The white rings are miracle synergy spots.  Some miracles, when cast near one of those rings, give a more powerful effect (heal for instance) than they normally would.

Some of the descriptions of the things available to purchase seem no longer to be available, and I can only assume they've been patched out. 

Can you elaborate on this?  If you hit X on your Xbox controller when in the merchant screen, it will give you a more detailed explanation of that item.

It's true that the game doesn't fall all over itself to give you information, which can be a hindrance.  But once you get into the right mindset, it will start to click.  Sounds like you're there already.

The guy you freed is named Lautrec, and once freed he will relocate to Firelink, near the Fire Keeper's cell (just head down the slightly concealed stairs near the bonfire).  After you talk to him there, he will be available to summon at a couple points later on.  I won't say anything more about him for now, but if you want to hear more just say so.

By item damage do you mean how much damage a weapon does?  Or do you mean durability?  Durability will degrade over time, but does so very slowly and can be repaired.  So it's not really a concern early on.  Repair powder, which is what I think you were referring to, isn't a bad thing to carry around for emergencies though.  You use it by equipping it in your item belt, then using it with X while holding the weapon to repair in your right hand.

Helmut the burg merchant sells the bottomless box (only he sells it and there's only one) and a repair box yes.  Buy the bottomless box, don't buy the repair box.  You don't really need it right now and can get it cheaper from someone else later.  Your human status doesn't matter as to what inventory merchants offer.  Are you certain he doesn't have it?

You have a stat called max equipment burden.  Weapons and armor, all having weight, add to your current burden.  The stat screen shows it as: CURRENT/MAX.  The closer your current burden is to your max, the slower you will roll (and run).  Your current roll animation is affectionately called the "fatty roll."  Your roll speed does not gradually decrease with more burden however.  There are a couple of discrete breakpoints.  25% or less of max and you'll fast roll.  50% or less and you'll medium roll.  Over that and you're a fatty.  If you exceed your max burden, you can't roll at all nor can you run.

That effect you're seeing is one of my favorite things about the game.  As you've noted, you'll see white phantoms running around periodically.  They have a generic appearance except for their weapons.  These are real people playing the game who are in the same area as you.  The cool thing is that the nearer they are to a bonfire, the less ghostly they appear.

Cracked red orbs let you invade someone else's world, with the intent to kill him.  The downside of these is that if you die you lose your souls the same as you normally would.  They're also in limited supply unless you join a certain covenant.  There is an item you can find later in the game which will allow you to explicitly summon someone to your world for a duel, and it has unlimited uses.  There's also of course the coop summoning mechanism.  In order to hook up with friends for either, you need to be at roughly the same soul level, and even then it's sort of a crapshoot as to whether you'll be able to find one another.  However, on the PC version there is a program call DSCFix I think (not to be confused with DSFix, which you're using right?!), which greatly improves the odds of connecting with friends (I think it uses the Steam friends list).  I haven't tried it yet but I hear that it works smashingly.  What's your soul level?

If you entered Darkroot via the Undead Parish, then you met Andre the Blacksmith right?  Andre is your friend and arguably the most important merchant in the game.  You will likely visit him many times.

There are of course other ways to get to Darkroot, but they're more difficult and/or inaccessible without a certain item.  There are some very nice items to be found there.  The simple fact that you've made it to Darkroot is cause for celebration.  It's not a trivial matter.  Good hunting.

It's also helpful to just observe a boss's behavior for a bit before committing to aggressive action.  Unfortunately, that can often mean getting killed.  But then, that's a part of the experience.  There are exceptions, to a degree at least.  Capra Demon comes to mind.  That fight is decided in the first 5 seconds, even if it lasts much longer.

I'm torn on the wiki thing and I'm probably repeating myself here:  While I agree that I may have never uncovered some parts of the game unaided, I missed out on the joy of discovery in some cases as well.  It's a tough call with no one-size-fits-all answer.  A lot of times my decision boils down to whether I'm going to play a game just once or multiple times - hard to know up front.  Given what I know now, I probably would have avoided the wiki much more often, albeit not completely.

P.S. there is an easy mode for the butterfly, but it's easy to miss and you must be in human form.

Witch Beatrice's oddities during that fight are a well-known annoyance.  When she hits with her soul magic, it's devastating of course.  Getting her to actually engage is the annoying part, as you found out.

Havel is a tough out.  Well done.