Are these sentences correct?:他们踢足球。汤姆跑过踢球。

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他们踢足球。is right.
汤姆跑过踢球。 is not right. You can write it in English and I will translate for you.

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they are playing soccer.       他们“在”踢足球。
Tom comes and join them.   Tom 也跑过来踢球。
Is this what you want to express？

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他们在踢足球，汤姆跑过来踢球

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他们_踢_足球。-- correct
汤姆_跑过_踢球。 -- wron

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汤姆跑来踢球。