Cares element

Spending a lot of time at your partner's place could affect your Housing Benefit, but it depends on whether the DWP considers you to be living together. There isn't a set number of nights that automatically triggers this change, but if the DWP believes you are living together as a couple, it could impact your benefits. 

The main thing is do you have "intention to return" So if you know you're planning to return to your house, then it shouldn't be a problem. But if the DWP think you've all but moved in, they may stop the housing help.

Yes, your partner could potentially get the carer's element of Universal Credit even if you don't live together, as long as they meet the eligibility criteria. The key factor is whether they spend at least 35 hours a week caring for you and whether you are receiving a qualifying disability benefit.