For the duration of the fight, creatures in the immediate area will not be visible to you (but they may still attack you if they wander too close). Keep in mind that other players will still be able to see you and attack you if you are eligible for player vs. player (PVP). Other players will also be able to view your pet battle in real time, including the pets involved as well as their health as the match progresses.
With the Classic beta now out it seems every related article somehow manages to spark the eternal war of "Vanilla was the best WoW sucks now" and "lol nostalgia goggles, Vanilla sucked, enjoy your two weeks of Classic". I have to say, even though I understand the principles behind the battle and the reasons people behave and talk this way... I actually REALLY don't get it on a deeper level.
Keep in mind that these quests are optional, and are not necessary to continue leveling and capturing companions. They are also account-wide, so if you complete the quest chain on one character, you will not be able to complete it again on another. However, any progress that you've made will be saved and you can pick up where you left off in the quest chain on another character. The dailies that you've unlocked will also be accessible by all your toons.
They seem to have expected some things, though, see adding pets with aquatic damage (gun and ooze) aswell as a resistant cockroach to stop us from cheesing everything with elementals. Yet, a fact their damage output is low combined with shields not checking for racial damage means this mechanic prevents a lot as you mentioned. The last boss has got an ability to remove basic shields so perhaps that was not in oblivion either… unlike the reactive damage. Also, an ability that forces swap altogether with an ability which prevents from being swapped, including critters? I can't say I like it.
Occasionally it's also been proposed to re-randomize all the gear. We didn't have best in slot lists back then. People weren't starting out as a fresh level 1 character with a complete list of which dungeons to run at 60 in order to gear as quickly and efficiently as possible. Now, all that data is available. If gear were re-randomized then all of those lists would become useless and thing would be close to how they were. Which is a more important part of the "vanilla experience?" the fact that item X from boss Y has exactly Z stats on it, or the voyage of discovery? Personally I think that voyage is way more important. Do you remember how many points of which stat on the ring or whatever that Darkmaster Gandling drops? I don't. Would it kill your experience if the BiS for every class were in a different dungeon so people had to actually play to figure it out rather than simply consult a spreadsheet? I don't think it would. For that matter, it probably wouldn't be a bad idea to handle it intelligently so that the better gear is in later dungeons. I remember there because some weird cases where level 40ish gear was better than anything that dropped in level 60 dungeons.
But how do you proportionally resize the swing? Even if you did, it wouldn’t give you the same type of joy as when you were a kid, because you have grown up and changed. Even if that wasn’t the case for you, you have to consider that the swing has become a place that is sacred for many other adults. When they visit, they aren’t visiting to try out the new adult-swing. They want to try the old swing. The one that brings back the joyful memories of distant past. They know that the experience isn’t the same, but if they close their eyes ... even for a brief moment ... they just might get that nostalgic thrill that brings them back to a time where things seemed so much simpler.
To me, certain character limits tend to be problematic not because of the length of actual content, but because of formatting tags and embedding taking up a lot of characters. This is something I experience on most of websites, not just this one, but the most aggravating issue over here is linking to user profiiles and other sources of strategies, which could be alleviated with internalisation of link paths and @mentions.
Each battle that you win will yield experience for each pet that participated. However, deceased companions will not receive any experience (so make an effort to keep them alive by swaping in a different pet). Experience gains are based on your pet's level compared to the wild pet. Defeating a higher level opponent will grant more experience than a much lower level one, but be ready for a tough fight!