Hey, the best place for you to visit is Delhi Hatt, Kirti Nagar and this might be out of your rout but there's this store in crown interiors mall in Faridabad which has Mr.DIY on the first floor with prices so low you won't believe. This store is my personal love at first site, you will find almost everything here.
Not possible you can try any other furniture markets like kirti nagar market
You can buy them online as there aren't any stores in Delhi.
No there is no ikea store in Delhi
No IKEA store in Delhi. Only store is in Mumbai and Bangalore. So you can buy online from ikea store if it delivers at your place or otherwise you have to go with the other options