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.
Zygor's Leveling Guide for The Elder Scrolls Online (PC Version) is an in-game, software based, strategy guide that will show you the quickest way to level your characters from 1-50. You can view and use the guide directly inside the game without having to print out anything or view the guide in a browser. This also means that our guides are dynamic and can track your progress in realtime.
I recreated my very first character -- a human warrior, because in the last-push alpha test I joined in 2004, there was no Horde -- and logged in. Immediately, I was surprised by how good the graphics actually looked, for being 15 year old textures-on-polygons. Warcraft's bright colors and cartoony aesthetic continue to this day, so all the increased resolution and better-contoured characters in Lordaeron don't really change the game's visual aesthetic.
If your pet's health gets too low or its attacks aren't very effective against a certain combatant, you can always switch out your current pet with another companion on your team. Only pets that are considered active (i.e., those in your three Battle Pet Slots), may be switched in and out during the battle. Once the match is over, you can always change up your active pet team, which is useful if one of your pets is low on health or dead.