Please correct the sentence, if i'm mistaken.

我想说好汉语。I want to speak Chinese well

Please correct the sentence, if i'm mistaken.

我要说汉语很好。I want to speak Chinese well

我想要把英语说得很好

Hi, Elena. I'll try to explain some of the corrections for you incase you are confused.

From your Chinese sentence, it seems like you wanted to say "I - want - to speak - Chinese - (very) - well.", if you look at each word individually. 好 is the adjective "good"; you wanted to say the adverb "well" (you are using the adverb to describe how you are doing the verb "speak"). In English we often add -ly to adjectives to make them adverbs (adj: quick | adv: quickly), but of course there are adverbs that aren't made this way (like "fast" or "well" in your sentence). The particle you want to use to turn an adjective into an adverb (like -ly in English) is 得. Looking at Linda's sentence:

我要把汉语说得很好。

You can see the pattern is [verb] 的 [adjective], with 很 added in this case. There are different places to add the object to the verb (汉语 in your sentence) and you can also repeat the verb, but I won't bother going in to detail.

You've also seen 要 changed for 想 and 想要. The problem with 要 is that it can mean "going to" and "need to" as well as "to want", and when it's followed by a verb, I think it's usually interpreted as "going to", mostly. Using 想, however, is different. It also means "to want" (or "would like" as it's a bit softer). You have to use a verb after it though (which is 说 in your sentence), like Angel did:

我想说好汉语。

Here the 得 pattern isn't used and 好 is used just before the object 汉语 as an adjective (I - would like - to speak - good - Chinese)

When 想 is used in front of a noun it means "to miss" (e.g. I miss you) and can also mean "to think" (e.g. I think that...). 想要 doesn't have this problem.

And finally 把 is used to move an object forward in a sentence

If this makes no sense to you, just stick with using adjective to describe nouns (like "Chinese") and not verbs (like "speak") for the moment.