Is Self-plagiarism allowed in two submitted articles by one author? Is it allowed that someone use the same paragraph in two submitted articles for two different journals? Note: both of these articles are unpublished still so it's not possible to cite one in another one. Also, those articles are submitted concurrently. If it is considered self-plagiarism, it should be really avoided or not? Because when someone works on a topic rigorously may introduction or even materials and method section will be relatively the same as his/her previous works. Any idea or suggestion is appreciated.
If the method is taken from elsewhere you should cite the protocol, and use block quote if necessary. If the method is novel, then pay attention during the submission, you should see one common question asking if the work has been presented or circulated elsewhere, you may use that to declare the potential repetition and let the editors decide. If no such slot exists, it's better to inform the editor in the cover letter.

Moving forward, consider cascading your publications: while paper A is under review, paper B should be being finalized, paper C being drafted, paper D's experiment being done, paper E and on being conceptualized. That way you can avoid problem like such and still maintain a reasonable output level.

To be honest, if I saw two papers from the same author saying "education data were broken down into 3 levels: less than high school, high school completed, and college or above." I will not jump off my chair and scream "plagiarism!!" But people's ideas about this issue are not all the same, I'd agree that assuming the worst would be a good approach.