Translation:My son wants to achieve success in swimming.
Are the pronouns ja and on frequently used with these verbs chcę and chce since they sound alike?
I've been thinking about it- according to the rules I've found, both sides of ę/e discussion state that you should pronounce clear ę to make distinction between words like this.
I personally would not use "ja" in a sentence I wouldn't use "ja" with different verb. I would rather say "chcę" or even "chcęł" (which is incorrect overpronounciation) while I usually just say "chce". but usually you can tell from context. And usually if you can't tell from context it may be a situation you would use "ja" with other verbs.
I guess yes, they're more likely to be used in situations when 1st person and 3rd person only differ by e/ę.
But a Polish ear can hear a difference between chce and chcę? Or are they essentially pronounced the same? Does it depend which part of Poland one is from?
It may depend on the part of the country, but also on the individual - I have stated somewhere already that my Ę is usually clearer than for the most people, up to the point that my pronunciation draws attention.
Theoretically, in standard Polish, if Ę is the last sound of the word it sounds almost as normal E.
The situations when there's need to repeat what you said because the interlocutor didn't catch whether you meant 1st or 3rd person are rather rare.