They are both grammatically correct. However, "I did play soccer" has an emphatic effect. It would more likely be used in a situation like this: Andy: No, you didn't play soccer. You: I did play soccer! If you are just saying (in a general sense) that you played soccer, use the first one, "I played soccer".

The usual form of the past simple is 'I played'. For example: What did you do yesterday? I played soccer. Did you play basketball? No. I played soccer. What did you play last Saturday? I played soccer. The form 'I did play soccer' is only used for special emphasis, especially when you want to contradict something that has been said: You didn't play soccer last week. Yes, I did play soccer! In other situations, you need to use the standard form 'I played'. I hope that helps.

Technically, both are grammatically correct, but which one you would use depends on the context. For example, when telling someone what you did on the weekend, you would say "I played soccer". However, "I did play soccer" would be used to emphasise it, as if someone said "you didn't play soccer". Hopefully that's cleared it up for you.

Yes, both are correct.