Question: Good Chillers and Filters? Water hardness.

I have a 20 gallon (~75L?) tank. I have a chiller/heater and a filter. The chiller was on the cheap side around 125 USD...and it's a really confusing one. I spent a while trying to figure out how to get it to chill the water. The chiller reads in Celsius, so I'll talk Celsius instead of Fahrenheit (which is what my country uses...). The reading at first was 19, okay fine...would prefer it to be 16-18, then it starts to increase to 20->21->22 (stopped there, thank goodness) and took me a while to figure out how to change the temperature to make it drop back down to the range I'm comfortable with. And it struggled to get below 20.

Right now it is at 16 degrees, which I'm extremely happy about. But I'm worried it is going to go back into the low 20s again, which stresses me out.

What I'm getting at, is...I need to find another one that is a better brand because I don't think this one is good. Would like one that can keep the tank in the 60's (Fahrenheit) when the outside temperature is in the 90's.Then there is the fact that sometimes the outside temperatures go to 20 below (Fahrenheit btw) or lower. I don't care if the chiller reads in Celsius or Fahrenheit, I can deal with either.

I also have an Aqueon filter that I believe is low powered, which is good. Is that a good brand? I got it at my local aquatic pet store. It stopped working yesterday but started back up for some reason. I was about to go buy another after trying to "fix" it myself when it started back up. This worries me.

If it stops working, am I able to not have one for a short amount of time if I wash the tank more often? The chiller moves the water around a bit too so the water isn't just "standing".

Any other suggestions on keeping the temperature in the tank in the 60's (16-18 C)? I'm planning on getting some blinds for my room as the pull down thingy fell off of one and the other won't stay down.

Also, my water is hard, any suggestions on lowering the water hardness naturally? I read peat moss and I'm going to go pick some up

I can't recommend chillers, as I don't use one, I use a couple dozen frozen water bottles, that I change out through out the day.
But for filters, you'll probably want a canister one, they are more powerful, and Axolotls need that, their waste is much more than fish, and so it effects water much faster. If you use a spray bar with the filter, and face it towards the glass, you won't create a current, so the Axies won't be disturbed.
I purchased this one https://www.amazon.com/gp/product/B0002DJ9NY/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
it includes everything to set it up. It is also adjustable, so no need to have it running at full force for a 20g, if you get the larger capacity, it can grow with you if you upgrade your tank size.
You may want to buy some Fluval bio rings or something similar.
I also recommend Seachem purigen, it works way better than charcoal, and can be reused over and over. Buy the canister and a few of the "the bag" bags, many reviewers have said the prepackaged bag split and spilled the purigen all over their tanks. I know it seems pricey to buy it separately but, it can be recharged and reused so you won't have to repurchase, probably ever.
When you say hard water , have you tested ph? Because Axies prefer hard water, people with soft water have to supplement their water to keep Axies healthy. I wouldn't do anything to soften your water, Axolotls can handle a pretty varied ph. My ph reads 8.2 straight out of tap, but reads 7.8-8.0 in aquarium. The ph of the water in the tank will naturally reduce on it's own over time. Unless your ph reads higher than low 8's you'll probably not need to do anything. Peat works for lowering, but also makes water tea colored, driftwood works exactly the same, and also stains the water. The Purigen can remove the staining, once the peat/driftwood is removed.