Taking a damp cloth and rubbing the inside of the cat's ears will remove most ear wax easily. The ear canals of a cat go horizontally inside the skull, so there is little to no chance that you will start poking inside your cat's brain if you wish to dab at the structure with a cotton swab, but a damp cloth is usually more comfortable for both you and the cat. The thin hair around the base of the ears is a perfect place to check for insect problems due to the easy visibility. All pet stores carry various types of scratching posts at reasonable prices. The friction on the scratching post erodes the edges of the nail and makes it comfortable for the cat to walk as well as keeping them clean and free of infection.
Most vets encourage the owners to clip their cat's nails every month or so.
This is a small blood vessel that will bleed if cut, but a septic pencil will seal it quickly. It does NOT extend to the edge of the nail, so there is plenty of room for you to cut safely. Check your pet's nails and feet regularly for any breakage or injury - a small papercut can easily become infected within days of the initial injury. Watch how your pet walks and be attentive to any shifts in behavior or activity. If you see any cloudiness or other factors, take your pet immediately to the vet.