Answer
(Fatwa: 1183/932/D=1431)
You are right. These are baseless talks. The name Maryam is very good and blessed one. You can keep this name without any hesitation.
It is forbidden to keep the picture of living beings inside house, because it prevents the angels of mercy to enter in house. Do not accept such gifts which contain pictures.
(2) It is allowed for the girls provided the dress is not exclusively worn by people any particular religion and it is meant for comfort and easiness not for fashion.
(3) If it falls in your residential part (i.e. the part that is in your use) then you can stick a paper on it or any flowery sticker. Convince the owner if he has any objection.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband