"A girl is swimming in a pond."
The simplest explanation i've seen is that が is usually used to emphasise the word/phrase before it. Andnは is used if to emphasise what comes after it.
Its best not to worry too much about it. You just get a feel for when to use them after hearing enough examples. You will hear certain recurring phrases always using が or は.
は and がare confusing for everyone but mostly がis used for emphasis . Don't worry you'll get there with practice .
It also helps that は is used for general statements, and usually が isn't, so that helps in phrases like "Books are heavy" and the like.
You're introducing new information, in this case a girl. It's harder to glean from these sentences because a lot of は/が usage functions in the context of the conversation which Duolingo lacks. So it's fine to not get quite why here.
You may think of it as follows: - xy が simply marks the subject of the sentence. - xyは indeed puts some emphasis on it. It's like saying "as for the cat, it's in the kitchen", pointing out that it's not dog you're talking about. It also works, if you ask your friend たなかさん about his intentions, feelings, etc.. Consider this dialogue:
[たなかさん]: "かわ に あるきます"。 The first sentence points out that you talk about your plans for t o d a y. The second simply throws the ball back to Tanaka (literally "What about you?". --> Just in case you don't know yet, the perfectly normal way to address others during talking is to say his/her name. But あなた は should be fine also, at least if you don't know the name.) Generally speaking, if you can think of the sentence as "concerning xy,..." or "as for xy,..." or the like, then you should use は.It works for about 90 to 95%, since there are some minor exceptions.
Do you mean suiei? Suiei is the noun form. Oyogu is the verb. Normally you say suiei when you want to say swimming is my hobby or i like swimming. Oyogu is for the act of swimming.
The verb you used does not exist.
泳いでいます (oyoide imasu) = is swimming
泳ぎます (oyogimasu) = swim
Yes - as IsolaCiao says the verb is 泳ぎます （およぎます). Also please see above for an example of a Japanese word unnecessarily written in katakana - 本当（ほんとう) not ホント.
いけで女の子がおよいでいます。(there is a girl swimming in a pond)
いけで女の子はおよぎます。 (some girls often swim in a pond)