"There are many flowers blooming in this park."
Hi, ignat980. You use います here because the grammar point 「verb[て] + います」 means this verb is currently happening or has been happening for some time. So, さいています uses the て-form of 咲く（さく）and the verb いる (or います) to say it is currently blooming as opposed to saying the flowers will bloom, which would just use 咲く（さく）。
Also, if you were saying, "There are flowers," you would write: 「花がある」 or 「花があります」, because ある (or あります) is used for inanimate objects.
I hope that helps! :)
This is a heck of a sentence. Here's what it's giving me as the correct answer: この公園は花がたくさんさいています。And here's what I've gathered from it so far - these are just educated guesses, but I hope they help:
Why is で or に not used? Because この公園 is the subject, rather than a prepositional phrase in this sentence.
Why is を used instead of が？ Because the "there are" is the dominating predicate (verb part of the sentence), not the "blooming".
Hi, Arien504795. で is used for when something, such as an event, is happening AT a specific location and the flowers are blooming AT the park. If you were saying that the flowers are existing IN the park, you would use 〜にいる or 〜にいます。As for your second question, が is used in the correct answer you provided here, so you're right that を shouldn't be used. I hope that makes sense. I recommend BunPro for learning more about Japanese grammar if you're interested.