Welcome to the forum - sorry to hear that
.
However, what visa exactly have you applied for? If you are not married yet, and are applying for a 6-month fiance visa to marry in the UK, then you should not be paying the NHS surcharge at all anyway, because the NHS surcharge only applies to visas valid more than 6 months.
What type of visa did you select on the online application form?
If it was a settlement visa and you were directed to pay the NHS surcharge, but you are not yet married, then it sounds like you've applied for the wrong type of visa. A fiance visa to marry in the UK (no NHS surcharge) is Settlement -> Settlement -> Marriage, but a spousal visa (with NHS surcharge) if you are already married is Settlement -> Settlement -> Wife (or Husband).
My question is whether or not I will be able to come in to the UK has a visitor, without a hassle at the border. I want to visit my fiancé for the period of one month prior to applying for my student visa. We are getting married in Belfast in August and have submitted the necessary forms to do so in Northern Ireland.
If you have been refused a visa, you should not attempt to enter the UK as a visitor without applying for a proper visa in advance.
Also, you cannot enter the UK as a visitor to get married... you need to apply for either a Marriage Visitor Visa or a Fiance visa first, because you are not allowed to marry in the UK if you only have a visitor visa - it's against the rules.
I'm a little confused about your visa situation though - are you trying to apply for a fiance visa to marry in the UK, or a Marriage Visitor Visa to marry in the UK, or a Student visa to study in the UK? You can't apply for all of them.
You either:
a) apply for a fiance visa, marry in Belfast, and then switch to FLR(M) spousal visa after the wedding, which means you don't need a student visa... you can study on the FLR(M) - although if you are not marrying until August, you likely won't get the FLR(M) in time to start your PhD.
or
b) Apply for a Marriage Visitor Visa to marry as a visitor in the UK, then return to the US to apply for a spousal visa, and then move to the UK on that visa... you can then study for your PhD without needing a student visa
or
c) Apply for a Marriage Visitor Visa to marry as a visitor in the UK, then return to the US to apply for a student visa and move to the UK on that visa... but student visas can take a while to be processed during the summer as they get very busy and August would be cutting it very fine - I would recommend applying for the student visa no later than July.