Question
when to fertilize and what kind and when live in illinois . the following ;  boxwood-burningbush-albertaspruce-weepingcherry-goldencypress  they are newly planted  and when to prune

Answer
Hello Richard

Wow - this is quite a question!

OK, first things first.  As these are newly planted specimens I expect that a good feed of organic or granular fertilizer was added to the soil at the bottom of the planting hole at the time, so no real need to worry about giving them more this time of the year as the dormant season is upon us - plantwise!

When signs of new growth begins to show next spring, an application of a general liquid fertilizer can be given.  A mulch of well rotted organic matter (leaf mould or garden compost) in mid to late spring might be beneficial.

If you have prolonged dry spells during the first growing season, water the plants liberally.  The evening is the best time to do this, so that the moisture doesn't just evaporate in the heat of the day.  

After the first year the plants should be stronger and more able to cope with the odd dry spell.  As they mature they will become more and more resilient and may not need feeding or watering by human intervention at all.

Pruning:

These plants are really easy to maintain and shouldn't cause you any problems at all.

Boxwood (Buxus) - prune in the summer to keep the shape of this plant neat.

Burning Bush (Dictamus) - strictly speaking this is a woody based perennial, so cut off flower spikes as they fade.  The plant may die down completely in the fall.  It shouldn't need pruning at all.

Alberta Spruce (Picae)  - Shouldn't require pruning at all.

Weeping Cherry (Prunus) - Remove damaged or wayward stems in late winter/early spring to keep this attractive plant tidy and symmetrical.

Cypress (Cupressus) - Give a 'tidy up' trim in spring.  Never cut back into old wood - the plant wont regenerate.

Hope this helps and that your new plants give you many years of pleasure.