Error in Process model .

Check this

https://community.appian.com/support/w/kb/271/kb-1046-no-valid-recipients-resolved-error-thrown-when-using-send-email

In Script task 1 you are getting recipients by rule!MSL_fetchDelegatedUserFromDelegationTable(originaluser :pv!emailRecipientUser) and storing in MST_PM_delegationtable(CDT),if the rule returns empty data then you are making recipients as pv!emailRecipients
so ,check rule!MSL_fetchDelegatedUserFromDelegationTable(originaluser :pv!emailRecipientUser) is returning data or not if no then then check value is present in pv!emailRecipients.

One more thing pv!MST_PM_delegationtable is single cdt value or array ? if single no need to use index[1] 

 you can get the user from cdt by pv!MST_PM_delegationtable.delegateduser

Thanks Krishna 

we are not getting any value from pv!MST_PM_delegationtable.delegateduser ....

and in pv!emailRecipients there is no value's 

then check the recipient user  is present in pv!emailRecipients or not,bcz to send email smart service  we need to give at least one recipient (recipients cant be empty )

if(
  and(
    rule!APN_isBlank(
      pv!MST_PM_delegationtable
    ),
    rule!APN_isBlank(
      pv!emailRecipients
    ),
    
  ),
  toemailaddress(
    "xyz@email.com"
  ),
  if(
    rule!APN_isBlank(
      pv!MST_PM_delegationtable
    ),
    pv!emailRecipients,
    pv!MST_PM_delegationtable.delegateduser
  )
)

if both values are empty then send the email to admin group or some one else or you can skip the send email node.

Can I cast the To field value to the emailRecipient type by using the toemailrecipient() function.

such as toemailrecipient( pv!emailRecipients )

if pv!emailRecipients  is empty then if you do toemailrecipient( pv!emailRecipients ) also that will return empty value..

so , it wpuld be good to change the type user to anything else or can we manually provide the email address for the particular user which we want to send the emails   

if both pv!MST_PM_delegationtable and pv!emailRecipients is empty, then manually provide the email address for the particular user or a group  which you want to send the emails

Thanks Buddy :) thanks for the help