Remathilis
Legend
Would dependent on what the skills or tools were. Let's try to follow our own system and just say "Int/Wis/Cha" based skills, sure. "Str/Con/De" based skills, unless the animal has proficiency with it, no.
"You also retain all of your skill and saving throw proficiencies, in addition to gaining those of the creature. If the creature has the same proficiency as you and the bonus in its stat block is higher than yours, use the creature's bonus instead of yours."
Sounds like any proficiency you get via Skilled or Resilient, unless the creature form in question has a higher bonus.
Lastly, my ruling on Mobile came from this.
"You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so."
Feat is another source. If a human can walk 10 faster than another human, I don't see why a wild shaped bear wouldn't move faster than another wild shaped bear.