Is the white spot fuzzy looking? I can't tell from the pics
How often do you perform a water change? Once every few months
What percentage of the water do you change when you perform a water change? Depends on how gross the water is.. fully when gross
What type of additives do you add to the water when you perform a water change? "Betta Basics" buffers the pH and promotes health
The first order of business is to change his water! Even if the water looks clean, there is ammonia building up and it can burn their eyes, gills and fins. If the level is high enough it will lead to ammonia poisioning and death. The only way to remove ammonia is by doing water changes every week, even with a filter. The filter will catch some physical debris in the water but wont do a thing for the ammonia. The general recommendation here is 2X a week -one 100% change and one 50% change. For the 100% you also want to clean out the debris like uneaten food and poop from the gravel. Add in clean water, add in the conditioner and then slowly acclimate the fish back into the tank.
Too much of a temp difference and it can cause him to go into shock.
If the filter current is too strong, you don't have to use it. A bigger tank, then yeah - you probably want a filter because it will do something called cycling which involved bacteria growing inside the filter. most people say anything under 5 gallons can't hold the cycle so I don't bother with filters on anything under 10 gallons. it will still catch some debris in the tank so if you want to use it, there are ways to slow down the water flow.
What type of food do you feed your betta fish? Regular food, came with tank
Like tropical fish flakes? You may want to pick up betta pellets - if nothing else they are alot less messy then flakes.