2. Is it ok to perform "the cross" after a prayer?
I rarely attend services at other churches unless it is a wedding or funeral. I went to a baptist service when I was a kid. I recall my Mom telling me not to take part in their version of communion (still don't know why).
As already stated, no communion except for in an Orthodox Church.
As far as making the sign of the cross, I see nothing wrong with it, but be prepared for people to give you an evil eye for doing something they consider "Romish." To clarify further what TheTrisagion wrote, the vast majority of Lutheran congregations do NOT cross themselves. You will find that more ELCA congregations will tend to cross themselves than LCMS congregations. DO you know which the church belongs?