One month ago, I have submitted a paper in a journal under Taylor and Francis. 3/4 days later after the submission, the status changed to "under review" and till now the status remained unchanged. I am in a hurry and need to get the final decision as soon as possible. What can I do to speed up the process? Should I send an email to the editor? How long it will be in "under review" stage?
You cannot speed up the process. Everyone’s in a hurry to get their stuff published so your own situation is repeated with pretty much every submission.
More importantly, what are the odds the manuscript will be accepted as is, with no revisions? Be ready to quickly make revisions, and be sure to address all concerns of the referees, and this will speed up the process.
3/4 days after the submission, the status changed to "under review" and till now the status remained unchanged. I am in a hurry and need to get the final decision as soon as possible.
If you are in a severe hurry, then consider whether or not you can post it to an e-print repository such as arXiv, bioRxiv, ChemRxiv, or even GitHub, or your own website. If you're in a hurry because you want to claim that you were the first to discover your findings, then this will solve your problem, except if the journal does not accept papers that have already been posted online (many journals these days allow pre-prints to be released with no negative consequences though). If the journal does not allow you to post it to a pre-print server, then consider re-submitting to a journal that does allow it, or if none of the journals in your research field allow it, you will have to consider what is more important: getting the paper published in a journal, or the hurry with which you need to claim credit for the work.
What should I do to speed up the process? Should I send an email to the editor?
The only thing you can do to speed up the process is to email the editor, but the editor will not be very delighted to see you rushing the process when the "normal" amount of time has not even passed yet, because papers take weeks to months (and sometimes over a year) to get published. You will come across to be demanding in a highly unusual way. Emailing the editor is an appropriate way to speed up the process when, for example, the journal says that referee reports will take on average 4-6 weeks to arrive, and after 7 weeks you still haven't received anything. It is very unlikely that rushing the editor right now will get your referee report produced within a few days: please accept that the time scale is usually best measured in "weeks" rather than "days".
How long it will be in "under review" stage?
If you tell us the journal, we may be able to help answer that for you.
If you don't want to tell us the journal, you can browse their website, perhaps under the "guidelines for authors" section, and see if it gives an estimated turnaround time for referee reports. If they don't give that information, you can ask politely to the editor, what the typical amount of time would be, but please understand that the amount of time you've waited is not an extremely long time in the journal publication world.