Quoting Kayleigh-louise Moran:" I bought a moses basket for the first couple of months of DD life, I also bought a swinging crib for ... [snip!] ... ive seen baby pillow cases do they need a pillow?And apart from sheets and blankets what else do they need in there cot?"
If the cot is bigger than the swinging crib, then no the sheets and bumper won't fit. You'll have to find sheets specifically for the crib. And if by "cot" you mean what we in America call a crib, then you'll have to check weight limits and suggestions. No, babies do NOT need pillows, especially for the first few months of life, they pose a risk for SIDS. You don't need anything except the sheet, and the blanket the baby is swaddled in. No comforters or any fluffy stuff in the crib, cot, cradle(whatever term you call it).