Could anyone identify the trailing plant with star shaped leaves in this photo please. And if you could tell what are its ideal conditions to grow
It's a variety of Hedera helix, common name Ivy, commonly known as English Ivy in the States. It's fairly forgiving and easy care, but it doesn't really appreciate lots of sunlight, it prefers shadier conditions. This one is variegated, which means it will need bright daylight to maintain its variegation. Water freely and don't allow the soil to dry out completely, but also don't leave it sitting in water in the outer container, empty out 30 minutes after watering.
It prefers cool to average temperatures, with reasonable humidity levels, so hot rooms, or anywhere near a heat source, are best avoided. Misting once or twice a week will help to deter spider mite infestation, to which this plant is prone when kept indoors. Responds well to cutting back which helps to keep the plant bushy, but that's best done in spring till early summer, though trimming off overly long trailing stems can be done any time. http://www.guide-to-houseplants.com/english-ivy.html
Yes that's some variety of Ivy. It could be: Mint Kolibri or Mini Adam. Ivy is fairly easy to maintain. It prefers to live on the dry side so before you water check the soil to see if its moist. You want the soil to be semi-moist; not saturated and not bare bones dry; instead, keep it somewhere in-between but leaning more towards the dry side.