There is no simple answer to this question. You want the soil surrounding the rootball to stay evenly moist - not too wet, not too dry. How often you may need to water will depend on your soil and your weather. And when you do water, the water needs to penetrate down the full depth of the rootball or deeper - at least 6-8 inches, preferably a bit more. The deeper the root system is developed, the less ongoing irrigation will be needed once the plant becomes established.

When should should i fertilize newly planted plants?

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If they are this years nursery plants, it isn't necessary this year, they've already done so. Wait til next spring when you start to see some new growth. I pretty much consider nandina a shrub, a light pruning if needed and one fertilizer app a year is all they get from me.

If you have a healthy, fertile soil you may never need to fertilize! The routine application of fertilizers is something that is promoted by the manufacturers of these products, not something that is supported by any horticultural authority. Plants get the nutrients they need for healthy growth from the soil and most amended garden soils will have sufficient quantities available without requiring much supplementation, especially when talking about woody plants - trees and shrubs like the Nandina. And even more so if you mulch routinely with a good organic mulch (compost, shredded leaves, even bark and wood chips).

Generally it is suggested to have a soil test done before determining when and with what to fertilize. Fertilizing when not necessary often causes more problems than it solves.

btw, when or if you prune the nandina, take the old canes back to the base, don't just trim back or shear the top. This will alter the growth habit and create an unattractive shrub. Nandina is a caning shrub and so will produce new growth from the root crown.

Thanks