Sasami, i do 20% water changes every weekend, I don't have a gravel vacuum. I've tried keeping bettas, goldfish, mollies, never lots of fish at once.
If you don't have a gravel vacuum, your water changes aren't actually as helpful as you might think. Go pick one up, it's pretty much necessary for a lot of aquariums. You don't have to spend tons of money, just go for a cheap one
. I've used the same one for years and it costed like $4 or something
I know you said that the tank is room temperature, but does that mean low 70's? Mid 70's? I'm not sure how warm your house is. Also, remember to measure the tank's temperature at night, when the lights are off, too (as it'll be colder, possibly too
Bettas are pretty adaptable, but it sounds like your water might be too alkaline
. However, if you fix any temperature/ammonia problems, you could try again but acclimate the fish very slowly. I would use the drip method, which is normally for acclimating sensitive animals. If you decide to try another betta, let me know and I'll give you more information.
Mollies do best in warm water (high 70's), so even if your tank was, say, 72 degrees, that might work for some tropicals but not mollies. Also, it's very difficult to find healthy mollies to begin with...they've been extremely overbred and inbred and are kept in less than stellar conditions. Granted, the same is true for most livebearers in the pet trade, but mollies are already more on the sensitive side. They fair very badly in poor water quality, so if you had any ammonia, that would explain any deaths. On a positive note, mollies do fine in alkaline water, so if you fix any other issues, you could try again. I've had the most success keeping them in brackish set-ups (a tank where MARINE salt mix is added), but your plants will probably only tolerate small amounts of salt. Mollies are also messy, so only keep a few in your 10-gallon (personally, I'd probably keep them in a 20 or larger). If you want the best chance of sucess, don't add any other fish besides the mollies.
If you love the look of mollies but are having trouble with them, try platies. They basically look like small mollies and are hardier, more peaceful, and do better in smaller tanks.
I wouldn't recommend even one goldfish for a 10-gallon. They're extremely messy and require really strong filtration and tons of water changes. Plus, even if you kept one, it would pretty much have to be your only fish (since goldfish enjoy companions, it wouldn't be ideal). Since you weren't vacuuming the gravel, that explains the death(s) and possibly even your ammonia spikes (when the gravel isn't vacuumed, uneaten food and fish waste sits in the tank and rots...when it comes to goldfish, it can get pretty bad fast).
With such alkaline water, you're going to have to be really slow with acclimation. Any interest in saltwater?
I can't think of any fish offhand that do well in alkaline water and can also live in a 10-gallon (our water here is totally netural, so I can't say I've had the same problem). However, I will think about it and maybe edit this post when I get home