I ask this, because I want to become a producer. Do they normally help write songs to kind of polish the song and get the most out of their clients? Do they ever make major changes to a song? Or do they stay out and stick to the recording/mixing process? Do you think any musical/songwriting talent will help me in becoming a successful producer?

Thanks, and sorry if this is the wrong forum
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What you need to do, and what you need to know, seems to depend on the what the client wants and needs. Some pop producers write and orchestrate entire songs for clients, while most rock/metal producers focus on getting the recordings sounding and feeling how the client wants them to sound. I would say learn all you can about music, including theory, song structuring, orchestration, as well as learning a few instruments. You never know what might come in handy.
Pink Floyd's producer, Bob Ezrin, had an impact on many PF songs, all the way up to the Divison Bell. I may be wrong, but I think he even co-wrote a few of songs on The Wall.
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Misha Mansoor produced Tosin Abasi's first Animals as Leaders album and rearranged a lot of the music alongside writing and producing the drum parts for the best sound possible.

It just depends on the needs of the client.
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The short answer is it depends.

Some producers do a lot of uncredited writing. "That song needs a bridge, what if we did blah blah blah" or adding chords, changing turnarounds, etc. Some, like Mutt Lange, take some songwriting credits. The line between producing a song and helping to write it can be very blurry, so by and large it's a good idea to have a mutual understanding before you go into the studio with someone.

As a producer, your job is to get the best version of the band's song on tape. Sometimes that means lifting up the hood and doing some serious work on it. Other times it's just being a set of trusted, objective ears. It can mean being a cheerleader when the team is down, or a taskmaster pushing them to find something in a take they haven't found yet.

Sometimes it's just knowing that something is missing. Sometimes it's knowing that something is missing and having an idea of what might go there.

Having an understanding of songwriting is, in my opinion, essential for a producer because at the very least you need to be able to speak the songwriter's language. You definitely need to understand music so you can help the band figure out what isn't working and suggest alternatives. That can be incredibly pretty general ("maybe hold something back on the first chorus so you have somewhere to go") to very specific and technical ("if you replace that E with an E7, and the bass steps down the scale in dotted eighth notes, you can then spend a measure on A major before the chorus starts again which will give it more forward propulsion.")

Most good producers know music very well. I'd be skeptical of someone who called himself a producer who didn't. But ultimately, the band is relying on you to guide them in the creation of their vision, not in the imposition of your own. That's a line even some very big names have, at times, struggled to keep track of. (Steve Albini on In Utero would probably be an example of that).

If all you're doing is the recording and mixing, most people would say that you're engineering the album, rather than producing it.
There is a book I can recommend that will give you a good overview of the possible tasks producers get involved in..."Recording and Producing in the home studio" by David Franz.
When I produce bands, and even for the producers I've worked with, it's all about what the music needs to meet the goal of the band. Sometimes that means helping completely rewrite a song, sometimes it's just being sure that the engineer captures enough sound/tracks to get the sound you want in the end.