You’re probably over-thinking this. As a US citizen you are eligible to use the eGates to clear UK Immigration, it is therefore quite possible that you won’t be asked any questions at all. https://www.gov.uk/government/publications/coming-to-the-uk/faster-travel-through-the-uk-border
If for some reason you do have a landing interview, the #1 rule is never lie Be prepared to explain, if asked:
- the purpose of your visit. Do not lie about your relationship
- how long you plan to stay and how you will finance your visit.
- if your boyfriend is paying for the trip, whether you have previously met in person (if he is financing your visit, getting a letter of invitation from him stating where you’ll be staying and that he is covering the costs may be a good odeaidea)
- what ties you have to the US that mean you need to return there at the end of your visit
- Your return flight plans (having a booked ticket is usual)
You can stay in the UK for up to 6 months per visit. UK Immigration Rules state that visitors must leave the UK at the end of their visit and must not live in the UK for extended periods through frequent or successive visits, or make the UK their main home. https://www.gov.uk/guidance/immigration-rules/immigration-rules-appendix-v-visitor The concept of ‘restarting the clock’ does not really exist, nor is ‘frequent visits’ specifically defined; typically the Rule is interpreted to mean that you should spend at least the same amount of time outside the UK as in it. Getting a visa does not change any of that.