How do I know what "kind" of goldie I have?

a basic guideline would be 20-30g for the first goldfish, and 10-15g for each additional. so that would be 1-2 goldfish for a 30g, 3-4 for a 55g, 5-6 for a 75, etc. whether you choose the high end or the low end depends upon the filtration you have for the tank and the level of attention you are willing to give it.

this is of course for fancy (round-bodied) goldfish, not pond goldies (torpedo-shaped). pond fish move much faster, eat better, and get larger than fancy goldfish. they should not be kept together, and pond fish have much bigger tank size requirements.

don't add a betta with your goldfish. bettas are tropical and have different needs than temperate-water goldies.

as far as sexing, i am not 100% sure, but i imagine that the gill spots would either appear at age 2-3 and stay there from then on or keep reappearing whenever the fish is in breeding mode. i don't think they show up once and then never happen again.

as far as what kind you have, a picture would help.

Your have a comet goldfish the shape of the head makes me want to say that it is a female but the picture quality is not good enough to be sure.

Round bodied golds (fancy's) have the split tail mutation (2 dorsal fins). This is called a fan-tail, veil-tail, and several other names. This greatly hampers there swimming ability and makes them very slow in comparison to the single tailed (more wild type).

As for sexing a goldfish once they reach sexual maturity they always show the marks.

Please don't keep a betta with Goldfish. Betta's do not do well with golds.

I did a quick search of all of your posts and have one major thing to say.

Please do some basic tank maintenance. You have just lost a lot of fish because of very poor water quality. This is because you did not do water changes. A low PH and Ammonia are just one part of the picture I imagine your Nitrates are off the chart. You have what is called "Old Tank Syndrome" which has weakened the immune system of all of your fish and killed some outright.

This is the single most critical part of taking care of fish. Please do at least a 50% water change with a gravel vacuum every week. If you live in any municipal system you will have to add dechlorinator to the water. Since you have a goldfish, your 30 gallon tank can hold only one comet for their expected life of 20-30 years. Any more than one and it is pretty much just a slow painful death sentence.
As you have not been doing water changes it is best to start off very slow. 10% every day for the next 2 weeks. This will allow your sick fish to adapt to the better water conditions.

Goldfish are very social creature and do better with a friend the the tank. As she is very small for her age (mine of the same age is closer to 9 inches -- you measure without the tail) she may have be a stunted form lack of space. You should also if your not already feed her pellets. Goldfish really don't do very well on flakes. They just can't get enough food before it dissolves into the water.

Comets are sold as feeder fish. As Flaringshutter and I can attest they are often very beautiful. I have one little lady in my tank now who is eight years old. She is about 10 inches long, white with long finnage. I got her out of a feeder tank. I also picked up some koi out of a feeder tank a few years back.

Testing your tank is really quite easy to do as long as you are not color blind.

The plant might have brought in a new species of bacteria and changed the ecology of your tank. With the fish already stressed because of the poor water condition it could be the "straw that broke the camels back".

Fishermen always measure from tip to tip and then add in another 15% for every year since the fish was caught. An eight inch rainbow caught on a worm becomes a 28" monster caught on a dry fly in 10 years or so. Of course the camera was broken so they sadly don't have a picture of it.

In aquarium fish finnage can vary because of selective breeding. Your comet has the more wild type of short fins. I have a mixture of short and long finned types. I have one fish that has a 5" body and 3.5" dorsal fins. Another is more like yours with a 8" body and 1.5" fins. You measure the body only to be able to accurately describe them.

I also would not get her another goldfish as a playmate. In order to add another comet you will need to have a larger tank. 55gallon minimum. If you want you can add in one mystery snail as a cleanup crew. I kept one once for 5 years in with my golds.

Hope this one makes it ... it doesnt look very healthy.