1) Yes, you will have to provide evidence of a genuine and subsisting relationship.
2) If you are married, there is no requirement to have lived together so you will not have to provide proof of this for the first spouse visa (Entry Clearance). When you go to apply for an extension later (Further Leave to Remain) you will, however, have to provide proof of cohabitation in the UK in the period since arriving.
I'm just a guy on the Internet who immigrated to the UK. My opinions are based on my experience and interpretation of the immigration rules and should not be considered legal or immigration advice; your mileage may vary.