We're a new group playing DnD 5e. Three of us have no prior experience (and I'm one of them, never played the earlier editions) whilst two of us have some to good experience with other editions.
I'm DMing Rise of Tiamat and I'm really struggling with giving the players any kind of challenge. We've got a Paladin with Sentinel and a Halberd, almost stopping everything in its tracks when they attack, a Wizard with Fireball (he might have found a spellbook), Minor Illusion and the Tiny Hut spell (which really messes up any kind of surprises I have in store for the night), a Druid which doesn't do much and a Rogue which died last session because of PVP (he got the option to sacrifice one player by an evil fountain spewing blood, he took it – and it didn't pay off in the end).
Just a bit of context.
My question is this: our Wizard is because of his familiar (a rat which he has on the inside of his robe) constantly throwing advantage on all of his D20 rolls. I said I won't allow this in the future sessions because the familiar needs and initiative, and also needs to somehow confuse or do whatever with the mobs to allow advantage.
He does, however, claim that the familiar gives him an advantage on all skill checks as well, in and out of combat. Is this according to the rules?