Also, the Gibbs Free Energy Formula is this: ΔG=ΔH-TΔS where the temperature is constant. I have some questions regarding why T is constant.
1) Since ΔH is present, heat will be absorbed/given out so won't there be a temperature change?
In a closed, system, yes. But we assume there is a reservoir for heat exchange. In such a case, endothermicity and exothermicity of a reaction effectively don't result in a temperature change, assuming heat conduction is sufficiently fast. Bear in mind, Gibbs energy is something of an
idealization. For most chemical reactions, the approximations are such that the Gibbs energy can give a good estimation of the thermodynamics of the chemical change. However in some cases - such as explosion chemistry - where temperature and pressure changes overcome the surroundings' capacity to compensate (and approximate as "constant temperature or pressure"), Gibbs energy is no longer so useful.
2) For ΔS one of the factors affecting it is temperature (Higher T=Higher entropy level) and when we raise the temperature the ΔS increases. And again the temperature increases from the initial state to the final state. So how can T be a constant?
Pretty much the same as above, although the temperature impact of entropy is taken into account in the Gibbs expression. Generally, we can assume that ΔS and ΔH themselves are independent of temperature, for small temperature changes anyway.