If we get married in Ghana, will it affect my fiance's entrance to the US?

While your your marriage in Ghana before your fiance's US entry on an F-1 visa might raise DHS' concerns regarding his intent, those concerns can be overcome with proper explanations. and your Ghana marriage should not have any negative impact on his eligibility to come to the US as an F-1 visa entrant. First, F-1 visa is a dual intent visa (that is, an F-1 visa person can come to the US even if the F-1 person also has an immigrant intent at the time of his F-1 entry. Therefore, if he is asked at the port of entry, he should honestly disclose his marriage to you and that at some point, he might wish to apply for legal residence in the US but that he has not made such decision and that you have not in fact taken any steps to that end including thre filing of an I-130. As to why he did not apply for immigrant visa instead of F-1 visa, he may reply that though, he is aware of his opportunity to do so, his academic pursuit is his main purpose for entering US at this time. If and when those priorities change, he may consider applying for green card or in the alternative, both you and him might relocate to Ghana. One way or the other, such decision has not and cannot be made at this time.

Yes. Once he is married abroad to a US citizen he will no longer be eligible for an F-1 non-immigrant visa since he has clearly shown "immigrant intent" which normally precludes him from entry in F-1 status. Assuming you marry him in Africa, you should seek options for consular processing him abroad for a spousal-based immigrant visa with the appropriate US Consular post in Africa [a complicated and lengthy process].

It should not if he already has his student visa, however, he may be presumed to have immigrant intent if he is married to a US citizen.

If he is married, there may be an issue of immigrant intent with respect to the F-1 visa.

Yes. Do NOT marry in Ghana. They will cancel the visa when they find out. You cannot have the intention to come to the US temporarily to student and also stay permanently to live with your US citizen spouse. If you are going to marry, do so after entering the US and waiting about 90 days.

It's possible the marriage my affect his student visa if immigration determines that your husband has a preconceived intent to remain in the US permanently after he enters as a student. In such a case, you will need to submit a relative petition on his become to sponsor him to the US. The petition is submitted on form I-130. above.