1.How can i limit number of characters in Textfield Profile Field?
You can't unless you apply javascript to each textfield on the page where they are used.
Why complicate things?? if you want to limit the number of characters you should be using a Textarea rather than a Textfield.
2.How can i prevent user from entering numeric value in Textfield and Textarea field to ensure user do not enter phone number.
Sorry, I have no idea!
3.How can a Member save message in his mailbox.
They can save messages by creating a personal folder and moving the messages there. Just add a note in the mailbox section about it.
Just make sure that you set it so messages never get purged in personal folders.
In your Admin go to "Features and Options" and look for the following option and set it to "0":
Purge old messages from member personal folders after how many days? (0 for never)