This question gets a bit tricky to answer... Starting from scratch, if you buy just vanilla WoW, you can experience the original world as it has been destroyed by the Cataclysm expansion. You can level up to level 60, but cannot access professions, areas, races, or other such things from any of the other expansions.
In order to access Outland, jewelcrafting profession, and Draenei? / Blood Elf races and starting areas, and level 61-70, you will need vanilla WoW + the Burning Crusade expansion.
In order to access Northrend, Inscription profession, and Death Knight class, and level 71-80, you will need vanilla Wow, Burning Crusade expansion, and Wrath of the Lich King expansion. Oh, and a prior level 55+ character on your account to play as a Death Knight.
In order to access the misc Cataclysm level 80+ areas, Archeology secondary profession, Worgen / Goblin races, and level 81-85, you will need vanilla WoW, Burning Crusade expanion, Wrath of the Lich King expansion, and the Cataclysm expansion.
Those are the restrictions. You can play on whatever realm you want with whoever you wish. You just may not be able to reach all the areas they can.
You can trial every bit of it with the 10 day trial, though I don't quite know how they treat it when your time is up.
Best Answer
It's simple: Timewalking events (for dungeons in past expansions) are ALWAYS Normal for the latest raid, which is now Uldir and with patch 8.1 will change to the recently announced Siege of Zuldazar. the Mythic Dungeon event (for dungeons in the current expansion) is ALWAYS heroic for the latest raid. Items can still warforge (+5 or +10 itemlevels), titanforge (+15 or more itemlevels), gain a socket or a tertiary stat (speed, leech, indestructible or avoidance) in accordance with the rules for the item the cache gives you. Currently, there is no way to get a raid finder or mythic cache.