Step 1: Analyze NAT behavior.
When a packet passes through a NAT device, the source IP address is replaced with the NAT device's external IP address to allow for communication with the external network. Hence, the Source IP is modified, making Option (1) TRUE.
Step 2: Checksum recalculation.
Since the source IP in the header is modified, the checksum, which is computed based on the header fields, must also be recalculated. Thus, the Header Checksum is modified, making Option (3) TRUE.
Step 3: Other fields.
The Destination IP remains unchanged, as it points to the intended external destination. Similarly, the Total Length of the packet is not affected by NAT translation. Thus, Options (2) and (4) are FALSE.
Final Answer:
\[
\boxed{(1) \text{ and } (3)}
\]