The homework involves reading a wristwatch, understanding time formats, and calculating arrival times and class start times.

The time shown on the wrist watch is 14:58.

$$\boxed{\text{14:58}}$$

The day of the week indicated on the wrist watch is SU, which stands for Sunday.

$$\boxed{\text{Sunday}}$$

The time 14:58 uses a 24-hour format because the hour (14) is greater than 12.

$$\boxed{\text{A) 24 hour format}}$$

The starting time for school is 07:30 am. This is a digital representation of time.

$$\boxed{\text{Digital form}}$$

"Quarter to four in the afternoon" is 3:45 PM. To convert this to 24-hour format, add 12 hours to the PM time.

$$3:45 \text{ PM} = 3 + 12 : 45 = 15:45$$ $$\boxed{\text{15:45}}$$

Calculate Lerato's arrival time at her register class.
Taxi picks her up: 07:00
Travel to school: 18 minutes
Arrival at school: $07:00 + 18 \text{ minutes} = 07:18$
Walk to register class: 5 minutes
Arrival at register class: $07:18 + 5 \text{ minutes} = 07:23$
Register class starts: 07:30 am.
Since Lerato arrives at 07:23, which is before 07:30, she will be on time.

$$\boxed{\text{Yes, Lerato will be on time.}}$$

Calculate the start time of the second period.
School starts: 07:30
Register period duration: 15 minutes
Register period ends: $07:30 + 15 \text{ minutes} = 07:45$
First period starts: 07:45
First period duration: 48 minutes
First period ends: $07:45 + 48 \text{ minutes}$
$07:45 + 15 \text{ minutes} = 08:00$
$08:00 + 33 \text{ minutes} = 08:33$
The second period starts immediately after the first period.
Second period starts: 08:33.
The teacher indicates the second period starts at 08:27.
Since $08:33 \neq 08:27$, the teacher is incorrect.

$$\boxed{\text{The teacher is incorrect. The second period starts at 08:33.}}$$