Hi, I'm a Christian

[Mister Agenda]

That is demonstrably false. Consider the following:

i. P (premise)
ii. P -> Q (premise)
iii. Therefore, Q (conclusion)

This is a valid logical argument; if P and (P -> Q) are both true, then Q must also be true. However, it is not necessarily true that the conclusion holds only if the premises do:

i. Barack Obama is in Washington, D.C. (Premise)
ii. If Barack Obama is in Washington, D.C., then Barack Obama is in the United States. (Premise)
iii. Barack Obama is in the United States. (Conclusion)

This, again, is a valid logical argument; if (i) and (ii) hold, (iii) must necessarily follow. However, (iii) could be true even if (i) and (ii) didn't hold; hence "(iii) only if [(i) and (ii)]" is false.

Yes, the conclusion can be true even if the premise is false. I presume in your example that Barack Obama is somewhere n the USA, but not in Washington DC. So your premise can be false and your conclusion true...by coincidence.