Does the eVisa for Thailand show the date of issue and is there an issue if activated after exit and re-entry?

Yes, the eVisa for Thailand does display both the date of issue and the validity period. Many travelers have successfully applied for their eVisa while already in Thailand, receiving approval only after their arrival. They printed the eVisa, exited the country, and re-entered to activate it without any issues. Immigration apparently does not have problems with this process, especially since the Ministry of Foreign Affairs is promoting the eVisa.