Does our existence cost us energy? When something needs to inform its presence, such as the electromagnetic presence of charged particles , or the gravitational presence of particles due to their mass. Is this made by sending information of its existence propagated in space via some kind of electromagnetic waves or hypothesised gravitational waves. 
So as a part of telling others of their presence to others, do the particles constantly lose their energy ? I understand that they could also gain energy in same way, but if a particle was completely isolated would it lose its existence and turn into pure energy over time ?
I understand that the mass and energy would together remain constant, but my question is that whether something would happen to a particle or would it remain a particle ?
 A: Energy in physics takes many forms, that can be interchangeable during interactions. The law of conservation of energy holds for a summation of all the different energy manifestations of the system under study.

if a particle was completely isolated would it lose its existence and turn into pure energy over time ?

No . An isolated particle can have energy as its rest mass, can have kinetic energy if it is moving with respect to some coordinate system. There is no way to transfer its rest mass energy anywhere,  unless through interactions ( and then it is not isolated) . An isolated particle is stable if it cannot decay to other particles. The electron for example, or a photon, can only disappear through interactions with other elementary particles.
You are probably confused by the simplified quantum mechanical picture of a charged particle continually exchanging virtual photons with other charged particles in the environment. Virtual photons are a useful calculational tool in getting the probabilities for the interactions of elementary particles. The virtual means that they do not conserve the energy momentum measure of their four vector, they are off mass shell, so energy conservation has no meaning in these exchanges.
In classical electromagnetism the fields of charged particles are stable, they do have an energy density but it is associated with the particle as its charge, and cannot be diminished by interactions. This is an observational fact. The boundary conditions of a problem with many charges will determine the composite fields, and any energy produced or lost comes from another form of energy than the field energy density of the individual electrons; it will probably be kinetic or potential energy to start with.
Macroscopically looking at live organisms, yes they continually exchange energy signals with the environment, energy which they have to replenish from other forms ( food).
Not elementary particles though
A: 
Anything when it needs to inform its presense such as electromagnetic presense of charged particles and gravitational presense of particles due to their mass does so by sending information of its existencs propogated in space via means of electromagnetic waves or hypothesised gravitational waves.

Not true. Maxwell's equations have wave solutions and static solutions. They are two different things. Similarly, the Einstein field equations have wave solutions and static solutions, and they're different things.

So as a part of telling others of their presense to others, do the particles constantly lose their enegy ?

No. Static fields don't transport energy.
