Will I have any trouble in immigration for getting a green card as my boyfriend said that he will not file taxes along with me?

I strongly recommend an appointment with a competent and experienced immigration attorney before you get married. He doesn't seem to trust you, but seems to be violating tax law if either of you claim to be single. Such a declaration is one issue, among others in such a relationship. You may be 'accused of' committing marriage visa fraud, which is a Federal crime, without knowing more facts. The above is general information, not legal advice, and doesn't create an attorney client relationship.

Best wishes for your upcoming marriage. Although not clear from your question, I presume your 72-year-old fiance is a U.S. citizen. It is not legally required for spouses to jointly file tax returns or to be of similar ages, but you correctly noted that a failure to file joint tax returns, and your and your fiance's age differences, may lead the USCIS to use a heightened level of scrutiny in determining whether you and he are living together in a bona fide marriage. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant details, could advise about preparing a persuasive marriage-based application notwithstanding the decision not to file joint tax returns.