Is the Military Tapping Phones?
It is technically possible to tap phone landlines (PSTN), mobile phones (PLMN) and computer internet traffic but this does not mean Fiji providers have installed the necessary equipment to do so.
An anonymous reader left a comment on the post "On the Alleged Phone tapping: Some Facts at Last" which helps to understand Telecom, Vodafone and FINTEL's Internet monitoring capabilities. He had no information on Digicel that also provides mobile phone services.
Call Details Records
Worldwide and in Fiji, all companies keep Call Details Records (CDR) that record the date,time,and duration of calls,and the names of registered callers and recipients.The records are mainly used for billing purposes, but they can also be used by police to track the contacts, location and movement of suspected criminals and the location of people in distress. With the proper authority police in Fiji can request this information from Fiji's service providers.
Telecom Fiji's landline network can be monitored ('tapped'). This is a feature built into the Ericsson system they use. The reader said monitoring was seldom used and access is limited to senior management and others who have a legal warrant.
Mobiles - Voice
Telecom's mobile network cannot be used for voice monitoring because it does not have the optional Lawful Interception (LI) feature which it considered too costly to install.
However, Vodafone Fiji has the technology to monitor mobile calls but I do not think they can listen in on conversations. Lawful Interception (LI) used for voice call monitoring is an optional feature of the Ericsson PLMN that Vodafone uses but their system does not currently support this optional feature.
Mobiles - Text messages
Records of Short Memory Services (SMS), a platform used for text messaging, are kept for several days by both Telecom and Vodafone, and can be "easily read." This makes texting a potentially insecure method of communication.
Internet monitoring by FINTEL's satellite or cable
All Internet Service Providers (ISP) can record what websites are visited by a username which in most cases is tied to a registered user. I do not think they can trace comments made by a reader to a particular website of use. It is, however, very easy to use a surrogate overseas ISP or website and so avoid possible detection in Fiji.
All this, of course, assumes the Fiji authorities wish to trace phone and internet traffic and have the time, manpower and expertise to do so, with or without the help of Telecom, Vodafone, Digicel and Fintel.
If tapping or tracking in some form does happen in Fiji, I think it will be confined to sporadic use and a few 'targeted' people. I very much doubt it is used on a regular basis or need be of concern to the vast majority of phone and internet users.