Hello shinchan

1- hard to say, everyone’s home and environment abit different. Have to slowly experiment. Depends whether your home has proper ventilation/insulation and other factors. Best in a fishless tank with your normal led light schedule and filter running, then record down somewhere. Ur equipment does expel heat. so less work if need to move around abit. Usually ground floor is best, more stable from temps fluctuation, good feng shui water energy. Most tropical aquarium fish can handle a slightly hot day. My tank is on the upper floor of my 2sto-house, with a big attic above it. Temps usually around 24 to 26c. No heater no chiller no fan no aircon. It just my aquariums in an empty upper hall. So I have a lot of open space and not cramped up in a room. The air gets a little humid and stiff but my tanks are cold to the touch. Just a  get thermometer or those tds meter 2in1 10in1 with temp sensor. You should be fine. Just take note the type of fishes you intend to keep. Some prefer colder water, some like most tropical fish abit warmer. And also usually bigger tank, more water, less temp jumping around.

2. If u have good ro filter, you don’t really need to treat your water for chlorine or any other trace elements. Good for easy water change maintenance.

Some would recommended you check anyway just to be sure especially for a first time setup, can also take this opportunity to check ur tap water to understand ur water more. Plus you may have to check water parameters after setting up aquarium, with the soil stones sand etc. water will change over time, doing regular water changes is recommended.

You may wan to get some gh kh powders to remineralize your tank. Ro water usually have close to 0tds ppms. Plants and fishes do benefit from them. And decent Kh can help buffer ur water ph from jumping around. Talk to your fish store owner to understand more. There are a lot of educational material on this online.

3. These equipment while not necessary. Helps when you need to troubleshoot what when went wrong with your tank. Like going to the doctors to do bloodwork before consultation. Checking tyre pressure before long journey.

You don’t have to invest much, cuz who knows you may quit after 2 months lol. Can always run to you pet store when you need em. Start with simple tank, grow from there. I think many try to jump deep end, then stress over maintenance and routine. You have ro water, so on that front your good.

Aux pump helps to oxygenate the water, I don’t usually use it in co2 planted tank or low tech tank. So buy them for big fish tank, koi ponds. Etc.

Talk to your fish dealer. Some fish are hardy, some you have to baby them. The latter more affected when water parameters change. Some prefer acidic water <7 some alkaline >7. So buffer them accordingly if you want to get the best environment for a particular fish or biotope. But can’t go wrong with 7ph ro water.

Most important part of fish keeping or aquascaping, is routine water changes and maintenance. So invest in buckets and some mini water pump to help with water changes lol. Will make this hobby much enjoyable. My first few months, I use to gravity pipe out to my window to flush out the old water from the tank. Imagine carrying buckets to up down the house to the drains. didn’t wan my toilets to clog. plan out how far from ur ro water filter to your tank, then tank to drain/sink whatever. If u somehow can pump straight from filter to tank. Your winning already.

Edit
Just saw ur pic, small tank no problem. No need all that fancy equipment, water change is easy and fast for small tank. Do like 20-50% enough. Just setup near the filter your good. Make sure you don’t over stock with fish. Feed less food and enjoy. Fishes in the wild, don’t really eat much. Enjoy my dude.

1- if you keen, should get a canister filter. Dophin 600 or so less than RM 100
2- do you inject CO2?
3- plant die- either not enoguh light, or not CO2. you should plant low tech plants if there is no CO2.
4 - plant rotting- will cause too much waste in the tank, the plant waste will become ammonia which then kill the fish. So that is the reason we need to condition the tank. This is done via a decent filter and sufficient bio media ( not neccessary expensive). adding bacteria could help in a way. Let it cycle for 3-4 days without fish and see if water got clearer.
5- using RO water- you should still put some anticlorine. you may buy the cheapest, but many of us using tensiongoon. and remember to add water and mix to a pail, wait for 10 mins before putting into tank.
6- Dont worry too much about waste/bio mass at bottom of the tank, you may never ever fully get rid of it- it will decompose gradually ( and yes bacteria help). The only think you can do is to avoid plant rotting,a nd avoid over feeding. if you see any large clump of plant rotting/or large leave dying- just cut it out.
PS: very nice betta, too bad RIP.
though- the tail rot could be bad water, it can be coz u mix other small fish witt it. Tetra might take a nip on the tail