Your PH is at a good level.
You will want to invest in a test kit for alkalinity or dKH (they are the same measurement). Knowing this will let you know how well the water conditions will be.
It does sound like your tank has finished cycling so that is a good thing.
You said the salinity was 2.020. How was this measured? With a hydrometer or a refactometer? If it was a hydrometer I highly recommend getting a refactometer. They are much much more accurate. Now, when you say salinity are you referrering to the value on the left side? Because on a hydrometer there is a salinity value on the left and the Specific Gravity is on the right. On these boards people usually refer to the salt level in terms of the specific gravity. And you would want your SG to be right near 1.025. So if you reading was for SG it is super duper high in salt.
You could have a quarantine tank with like a 20-30 gallon tank. In the tank you would just have the water, maybe a hang on filter, heater, power head or two. no live rock or sand. It is just designed to be temporary housing until you know the new fish you just bought doesnt have any diseases.
Yes, I would say you need increased filtration. Ideally with a tank the size you have you will want to have a sump, refugium, or a combination of the two. Something in the 30 gallon range. Bigger if you can. If you plan on having any corals you will also want to have several powerheads for increased water flow. How much live rock / live sand do you have? These also play a big factor in filtration. More is better.
I am not a disease expert on fish but I do know you will find a lot of information on ICH in the disease section.
Hope that helps a little bit.