Yes and yes. There's nothing in the TSA rules to say you can't. You can bring pliers up to 7 inches long in your carry on bags, even screwdrivers, so tweezers are no problem. Nail clippers are allowed because they aren't scissors more than 4" long. My other half carries small scissors all the time, she turns them out of her pocket in to the little change tray next to the metal detector and in a dozen flights nobody in the US or UK has said a word about them.
Check the TSA list instead of listening to people guess. Or ask the airline.
When I wanted to know the procedure for transporting firearms I went to my local airport and collared the TSA guy at their inspection booth. He was very helpful. Much better than finding out on the day.
According to the guidelines, you are not allowed to carry these items in your carry on luggage. But bringing these items with you is not always noticed.
It usually depends on what airport you'll be screened at. If you'll originate your travel at a smaller, regional airport, your tweezers and nail clippers will most likely not be confiscated. If they're packed inside a makeup bag which is inside another zipped piece of luggage and you look fairly normal, the screener is likely to let your bag through just fine.
P. S. -- I hope you're not planning on clipping your nails on the aircraft or in any public place. I would be very annoyed if you sat next to me and clipped your nails. The most logical choice: stow them in your checked baggage and clip your nails in the hotel room at your destination.
Noo they'll be taken off you at security. They're classed as dangerous and you could use them as weapons... lol
Why would you need to take tweezers and nail clippers on a plane.
Nope......You can load as baggage in a suitcase, but not into the passenger compartment.