Resetting up a tank

Are you testing the water for ammonia/nitrites? Adding fish food will work, but you'll still want to test to know when the bacteria colonies are large enough to consume the available waste, and it will be hard to control the ammonia level with just fish food since there's a time delay between adding the food and it decaying to ammonia.

What kind of catfish? Some are not suitable for keeping with small fish--general rule is long whiskers = more predatory. Many of the available cats will make a night time snack out of most tetras. For an algae cleaner, bristlenose are good--stay relatively small, and actually eat algae as adults (though they will need to be fed in addition to cleaning). A lower bio-load would be better--predators like cats are heavy waste producers, as are any large herbivores.

Plants are helpful, but not always required. Without plants, you can use nitrate levels to guide water change schedules--at a guess, 10% would be a bare minimum.

As long as you have chlorine, not chloramines, leaving the water in a tub for a while will work. Adding some agitation will help out and shorten the time needed to 'age'. It's possible that nitrogen is dissolving easier into the water in the pipes in the winter--or it could be CO2 levels raising (more likely, since CO2 will impact pH) as the water is under pressure in the pipes, and since water usage is often lower in the winter, it sits long enough to supersaturate. Either way, agitation will help.

Hi, welcome back to the hobby!
You're doing a 'fishless cycle' (providing ammonia with something other than live fish to cycle the tank) right now, good stuff You'll need to keep tabs on the ammonia (NH3/4) and nitrite (NO2) and, eventually, nitrate (NO3) levels to know how it's progressing, so you're going to need some test kits. It's a good idea to get a 'master kit' that gives you NH3, NO2, NO3, pH and KH. The KH is a good idea, since it sounds like you may have very soft water (if your pH is crashing, it's likely from CO2 and this happens more easily in very soft water).
Personally, I'm not partial to UGFs, especially if you want plants. I used them for years and I'm MUCH happier without. With a UGF you're going to want to vacuum the gravel with each water change to remove all the gunk trapped beneath the filter plate.
Weekly water changes can be much larger than 10% - honestly, 10% won't do much at all. Many of us change 40-50%. I find this amount works well for me - if you've got no live plants, you can use your NO3 readings as a guage; just change however much you need to, to keep NO3 levels below 20ppm. If you have a place to age your water, that's a great idea - unless your water supply contains chloramine, letting the water sit will allow chlorine to evaporate and you won't need to add chemicals to accomplish this. (If there are chloramines in the water, AFAIK you're going to need a water conditioner to make it safe for fish even if you let it sit).
Live plants are great, but not essential by any means. Fish don't really care if the plants are plastic/silk. If you've got enough light for plants (fluorescent light, 1.5W per gallon or more) and you're willing to fertilize them if needed, I'd encourage you to try it out. Most people who've made the switch from plastic to live plants say they'll never go back - they're a bit of work, but they're beautiful and much more natural looking.
For a small tank I'd recommend otocinclus affinis - oto cats - in place of a pleco. They keep tanks very clean and stay under 1.5" long. You'll want a few, they like company.
HTH

[edit] Looks like OG beat me to it - sorry for the repeated info [/edit]

Cories are a good choice--they won't eat your fish. Get more than one though--cories are social fish and will behave better (more interestingly) in a group. In a 20, you'll only want to go with 3, but they will appreciate having some buds around.

3 cories will put it close--you'll need to be careful sticking with your cleaning routine. Go with a smaller algae eater, like a pair of otos, or skip them entirely (algae can be controlled much better through good tank maintenance) and you'll be fine. For what it's worth, the advice on going with 7 tetras is usually sort of a myth. They do better in a group--the bigger the group, the happier they are. But, there's nothing magical about 7. Often, people will advise going with odd numbers because odd numbered groups 'look' better to us humans. The fish just know they have some buds and feel safer that way.