Hello there and welcome to the forum.

Sorry to hear that you were initially given poor advice and that one of the fish died.
You certainly did the right thing by researching your fish, then getting a heater and filter. Bettas don't like a huge amount of water flow, but filters are absolutely essential to build up the bacteria for the nitrogen cycle to deal with the toxins produced from waste. You are doing a great job so far and it's good to hear that your betta is looking better.
The first thing I'd suggest is to get a water testing kit. I use the API freshwater master test kit. It's not cheap, but can be bought cheaper online than in the shops, is more accurate than the dip strip tests, and lasts for ages. Your filter will be starting to build up bacteria for the nitrogen cycle, which will cause high levels of ammonia, followed by nitrite, so you will need to test for these and deal with them.
As you already have the fish in your tank you will have to do a fish-in cycle, so I've attached a link that will help you through it.
http://forums.thinkfish.co.uk/fishtank-filtration-and-cycling/fish-in-cycling-with-fish-how-to-do-it/As for getting a friend for you betta, they are fine on their own, but a bigger tank would be nice. It is possible to mix betta with other fish. I have my male betta in a 34 litre, 50cm tank, with a group of panda cory, and everyone seems to be getting along fine. I don't have any experience of female betta though, so perhaps some of the more experienced keepers will be able to offer advice on that.
As for other water parameters such as hardness, if you go to your water suppliers website you should be able to find a section on water quality, which will give a lot of information. The hardness will be listed under a number of units, and the german degrees of hardness are the ones usually used.
I hope that helps for now, just to get you started on cycling your tank and testing your water.
In fact, if you know someone with a tank that has a mature filter, perhaps you could ask them for some of their media to seed your filter and give you cycle a good start. If you don't know anyone else that keeps fish let me know as I am happy to send you some of my mature media, which should help to shorten your cycle.
Please keep us posted on your progress and let us know of any questions or issues, as we are more than happy to help as much as possible.
Best of luck.
