1. Are there also conditions in DnD which increase damage, like vulnerability to "wet" in BG3? If not I would not use "wet" in fights.
RAW, no.
BUT, DM's can allow interactions that seem fine. Like having a Rogue sneakily knock over an oil barrel so the Wizards Fireball creates a blaze for extra damage.
2. How many magical items are "normal" per character in average DnD campaigns? I think there is much less abundance than in BG3, but is there a hard restriction?
Depends on the DM/Campaign.
Usually, dungeons will have scripted magical items that the DM wants the party to find to give them boosts and to make things interesting. While there will often be vendors selling key magical items that provide critical benefits to builds.
Also, some DMs will allow enchanting and to varying degrees. Whereby players can spend gold to create magical items.
3. How common is it to multiclass? I got the idea from reading that multiclassing in DnD results in much more disadvantages than in BG3. I will probably avoid multiclassing (a hard blow to me).
Depends on players. Some players like to min/max and will abuse multiclasses and point buy their stats. Others will just play for flavour and will either stick to monoclass or will have some story based multiclass (More notably for one-shots where a party might start at a higher level)
4. How common are scrolls and potions? My inventory is filled with them, using them feels a bit like cheating.
Pretty common. Wizards can normally make scrolls when they long rest. Potions can be made by anyone proficient with medicine (Oh look, an actual use for that skill, who'd have thought?)
5. Can you respecc in DnD? Often, sometimes, one time, never, depends?
Typically no.
However, when a character dies, the player gets to make a new one to join the party. In such scenarios, they will often create a new class making it essentially a "Respec"
6. Haste is luckily toned down a bit in Honour mode, but I still don't like the spell. How common is it's use in a normal DnD campaign?
Haste is less used in normal campaigns. Mages tend to want to use every spell slot on Fireball.
Also, combat can last a while so the lethargy from Haste can actually make an impact. Since DM's will scale encounters to their party's power levels to keep things interesting.
7. I wonder how stealth now is compared to DnD. I think it's toned down compared to BG3 EA but is there something to avoid?
Stealth is WAY better in TT. Less for RAW but for all the things that you're allowed to do with DM permission.
Of course, BG3's in-combat Stealth is broken compared to TT. But outside of combat TT reigns supreme since you're allowed to do things besides steal/stab.
To say nothing of silly things people do. Like the story of an Orc Rogue who's "Stealth" was maxed out Intimidate and he'd yell angrily at people "I AM A TREE" and roll intimidate checks to see if people believed him.