If you wrote a good recommendation for someone else, there is no reason not to display it on your profile. This will display to those viewing your profile that you have worked well in the past with others, that you are able to show appreciation and give positive feedback, and that you are able to write cogently and effectively.
It would be nice if they ...
Not only acceptable, it's advisable. It is also allowed by Twitter- their page has tips on managing multiple accounts.
For your personal account, don't put anything in the bio or make tweets that identify your employer. That way if you do tweet about something controversial, you are speaking for you, not your employer.
Yes, you can (and you should) create a separate account to use in a professional manner (in work context). Many people handle multiple accounts to keep their personal and professional life separate in social media - it's not uncommon.
From Comment: Twitter seem to allow and encourage having multiple accounts.