Tongan is the official language but English is very widely spoken
There are several flights a week from Auckland and Suva.
There is a public bus system and a few taxis but Nuku'alofa is small enough to walk around. You can rent cars and motorscooters. A Tongan driver's license for T$15 is available and can be obtained at the police department with your home license. Outside of Nuku'alofa it's easy enough to hitch or you can hire a bicycle. Cycling the length of the island takes about an hour or two.
Toni's tour of Tongatapu is a great option on Sunday when everything else is closed. T$40 per person min. 4 people
Most restaurants and eateries are closed on Sunday but there are a couple of Chinese restaurants which are open Sunday.
Tongatapu is very safe but the usual travel precautions apply. Don't flash expensive cameras and jewelry and don't leave passports, money, clothes, etc. lying around in hotel rooms. If you're staying with locals (there is a high likelyhood you'll be invited to stay at someone's home on Tongatapu) take your valuables with you during the day and secure them at night
Tongan drivers are sometimes erratic so watch out. Asking for a helmet when you hire a bicycle is advisable. Dogs can be a nuisance especially in some areas outside of the capital
There are flights and ferries to 'Eua, Ha'apai, and various other islands. None of these services run on Sunday.