I want to publish some case studies from my customers on my website. Each case study will have real numbers about website traffic. I will also publish website screenshot. Do you think it is enough to get permission by e-mail?
1.) Is there a (written) contractual agreement between you and your client? (a.) If so, what does the privacy/data usage/advertising-publishing clauses say you can do with the data? There data may be considered (proprietary information or covered under intellectual property law) of the country/state they are located.
(b.) If not, then a contractual agreement for services and what you can/cannot do with the data that you create or collect on your clients behalf should be made or modified.
2.) E-mail as proof - In most cases a "E-mail" alone is not enough, (It is "supportive" of a claim but not sufficient alone) however in the United States an E-signature is recognized in most cases by the federal government if offered by them and in many cases by the individual states. The list of collective resources is too numerous to list here but an example of its criteria and acceptance is here: Government Paperwork Elimination Act (Sorry a lot of reading there)
3.) Why is e-mail alone not enough? Generally there is no way to guarantee that the e-mail is neither compromised or accessible ONLY by the person by whom you want permission from. That is the reason that many originating contracts (Those that require an original signature and or photocopy of ID or SWIPE of a credit card) will include a section asking for permission or notifying the contracting party of your "notification by e-mail" or "permission by e-mail" policy, that way they are accepting the risks of agreeing to using e-mail as a means of giving permission or receiving information.
4.) Basically if you don't already have contractual terms in place to cover this then use the e-mail to advise them of the permission you seek and ALSO advise them you will send a letter by standard mail for them to sign giving you permission to use there data. Lastly, add the appropriate clauses to your contracts going forward to cover this.