Minecraft – How to put a tamed toad in a safari net

As of the Minecraft version at the time of writing this...

Tamed wolves are not a passive mob and they do not have any limit, so they will not affect the passive mob limit (because if they were counted in the passive mob limit there would be a limit on the number you can tame.)

Passive mobs (a pig, for example) will NEVER attack you, even if you attack them.

Wolves are actually tame, meaning they follow and protect you.

Short answer:

Tamed wolves do NOT affect the passive mob limit in any way.

Yes, they can. I've gone into dangerous mines many times, thinking my dogs were safe and sound in my home, when I see one of them randomly teleport into the lava pit in front of me. To remedy it, (here comes the solution part) I usually make the dogs sit down because after that they won't move. At all. It's absolutely perfect for going to my obsidian mine, situated ON AN ACTIVE LAVA LAKE, home to the graves of many dogs.