Adding a little note to the "schwa" difficulty:
A Mexican friend of mine went to a record store in Chicago, and he wanted music by Harry McClintock; his English was slightly broken and his accent didn't help much, so the clerk asked him again what he wanted. My friend then went "maaahcliiinnntoohk". The clerk then said: "¿Usted es de México? Venga, las grabaciones históricas están aquí." Happy ending, but hard way to see how much he still had to learn.
I think your schwa thing is the same problem: Mexicans tend to make no difference between "sheep" and "ship" or between "must" and "most", because our vowels don't have any nuances. Similarly, American Spanish learners tend to pronounce vowels most of the time the way they would sound in English, which for our ears, that's as if most of them were /ə/ instead of a, e, i, o, u.
When they say something like "concierto", they'll probably pronounce most of the word as they would
in English, then we can't recognize the first "o" and it's likely that the last "o" will be barely audible.
That's why they change the vowels of a word when they write (like when "carretera" becomes something like "corretera"), or change a verb even when they know the right conjugation (like saying "tú quieras agua" instead of "tú quieres agua").
Since the speaker provides vowels with the nuances they usually have in his/her native tongue, the sounds become unrecognizable for the Mexican listener.
It's all a matter of dedication and practice. Most of us will never completely lose our foreign accents, but there are plenty of rewards when we have the certainty that we're easily understood.
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