You establish your contact with Imam e Zamana as
Even you don’t need to write and keep. Do wudhu, pray namaz e Imam e Zamana as speak to him and discuss your issue.
Sometimes when I feel like speaking to Imam E Zamana and discuss my problems with him, I write my feelings on a paper. Everytime it is not possible for me to put the letter in the river as it is recommended for an Ariza. so can I just keep the letters to myself instead of letting them in water? Will my problems reach Imam E Zamana if I keep the letters with myself?
Yes inshallah. If Allah wills he will read them