Yes, it is acceptable. On the other hand, some people feel it is bad style to "split" the infinitive by inserting words between the "to" and the root verb.
"Are we trying not to age" and "Shall we try not to age" have different meanings in English. Whether both are acceptable translations from the Czech original, I don't know. Maybe a native Czech speaker will address this in the future.
In 'shall we try', shall indicates a non-indicative state - the subjunctive. I don't believe the present as we've learned it covers subjunctive or other non-indicative types of statements.