L322 Couple of new owner issues.

Hi guys after 18 months of no range rover in the drive (had to sell old P38 Ruby) to help pay for daughters wedding I bought last week an 02 4.4 M62 engine Vogue with Primms LPG for spares or repair money. LPG has been serviced and now runs sweet as / just given her a complete service including gearbox filter and sorted a couple of little niggles out but there are a couple im still struggling with. Firstly passenger rear door wont open on the fob. It unlocks from inside and will lock on the fob but not unlock. Secondly it would seem that the rain sensitive function is not working. iv put it on intermitant as instruction book but still continues to wipe with a clear and dry screen. I have at present no Diagnostic kit for it but looking to buy something shortly. Any help would be appreciated and its good to be back !!!