to cross vs to have crossed

0A- He is believed to have crossed the frontier last night.02br
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00B- He is believed to cross the frontier last night.02br
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001. Are they equal in meaning?02br
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002. 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 01del00particularly that of derivatives of Past Participle verbs02del00 is quite difficult to distinguish from one another. "Broken" is an adjective, why not "composed"?02br
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01b00This poem is generally supposed ____ in the fifteenth century, but some people date it even earlier.02b02br
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00A) being composed02br
00B) to be composed02br
00C) having been composed02br
00D) to have composed02br
00E) to have been composed0-