One reason for being denied entry is: "using deception in an application for entry clearance, leave to enter or remain." This is, according to your description, your case. It does not matter what was your motivation. For some reason you thought it was a good idea, and the UK thought it was not.
The above situation results in an entry ban for 1 to 10 years. If you have used deception in an entry clearance application (which you have), there is a mandatory refusal for 10 years. That means that any visa application, for whatever reason, is automatically denied.
Source: https://www.gov.uk/guidance/immigration-rules/immigration-rules-part-9-grounds-for-refusal
Refusal of entry clearance or leave to enter the United Kingdom
(...)
(d) using Deception in an application for entry clearance, leave to enter or remain, or in order to obtain documents from the Secretary of State or a third party required in support of the application (whether successful or not);
unless the applicant:
(...)
(ii) used Deception in an application for entry clearance more than 10 years ago;
But yes, there is an exception. The ban must not be applied automatically in the case of family reunification under appendix FM.
However, that requires that OP's partner is British, earns more than £18,600/yr, among other factors.
Source: Immigration Rules Appendix FM: family members
The marriage would not pre-date the ban. The OP has a bad immigration record and has contrived to frustrate the immigration rules. That's not a good beginning. If she marries her partner, she will still have trouble proving that her relationship is genuine.
---------- UPDATE following comments ----------
You did not lie in your visa application, since you did not apply for a visa. But the rule says: "entry clearance, leave to entry or remain." You have lied when seeking a leave to entry, according to your depiction and the letter above. That does not change your situation at all.
If you marry your boyfriend, you could try and get a spouse visa. But you'll need to prove that your marriage is genuine.
If you were in the UK, you could apply for a ‘family of a settled person’ visa. Now you'll have to apply from abroad, paying a fee of between £100 and £1,100 (depending on the length of the visit), and no right of appeal if it is denied. There is a laundry list of conditions to be met, and documents to be submitted.
You should not put too much weight on the "they will be separating a family, which is against the law...right?" part. No, it's not illegal. And they are not separating you, they are just imposing conditions on you moving into the UK. You could marry your boyfriend and establish a family in Brazil. You have a right to family life, but it must not be established in the UK at the British taxpayer's expense.
Whatever you decide to do, you'll need to ask a solicitor accredited by the UK Law Society and specializing in UK immigration law for detailed advice and possible solutions.
