Is it possible to enter first on a fiance visa then do the civil partnership?
Yes, that is the purpose of the fiance(e) visa. A fiance(e) visa allows you to move to the UK, marry in the UK, and remain in the UK to switch to a spouse visa. The fiance(e) visa is valid for 6 months, so you must marry and submit an application (either by post or in person) within 6 months of moving to the UK with this visa.
Essentially, the options for moving to the UK when your partner (proposed partner) is a UK citizen are:
1. Get married outside the UK (ex. US). Apply for a spouse visa (from where you have legal residence, usually the US) to move to the UK.
2. Get married in the UK. Apply for a fiance(e) visa to move to the UK and marry in the UK. After the marriage, apply for a spouse visa to extend your stay (and allow you to work, and so on). You do not have to leave the UK.
3. Get married in the UK with a marriage visitor visa. You can apply for a marriage visitor visa to get married in the UK as a visitor. Return to the US and apply for a spouse visa to move to the UK. Note that a marriage visitor visa is still a visitor visa, so you must abide by all the rules a visitor must, including no switching to another visa category. If you want to get married in the UK and stay in the UK after, the best option is the fiance(e) visa.