A- He is believed to have crossed the frontier last night.

B- He is believed to cross the frontier last night.

1. Are they equal in meaning?

2. In addition to the one above, what about this question? "E" is correct. But my scruples are about "B" taking the "composed" as a participle adjective. Adjectives particularly that of derivatives of Past Participle verbs is quite difficult to distinguish from one another. "Broken" is an adjective, why not "composed"?

This poem is generally supposed ____ in the fifteenth century, but some people date it even earlier.

A) being composed
B) to be composed
C) having been composed
D) to have composed
E) to have been composed
1. Only A is correct.

2. Only E is correct.
He is the first man to climb Everest

He is the first man to have climbed Everest

They both seem correct