Welcome to the Forum! Congratulations on your lovely new house and yard!
Item 2 is boxwood, evergreen frequently used for hedging.
Item 5 is some kind of deciduous tree that will be much easier to ID once those buds open up and it has leaves and/or flowers.
All the rest are a variety of different evergreen conifers. Probably someone will come along who can identify them more specifically for you. But in terms of care, it really doesn't matter. There is nothing much you can do to care for a mature conifer unless your area is in severe drought (I.e. drought lasting more than a year). In that case you might try to save it by watering, but that would have to be deep watering, where you put the hose on low and just let it run for 24 hrs or so, moving it around the tree. Of course in that kind of drought, there might be water restrictions that would prohibit that. But all the action, in taking up water, nutrients, etc is many feet below the surface. Little you can do on the surface matters to them.
It helps to mulch around them to conserve soil moisture. You can give them fertilizer spikes once a year. Don't prune them unless and until you know what they are and what kind of pruning they can accept. Many conifers have branches that are basically dead wood inside where the needles are. If you cut in to that, they will not regrow.
The one in item 6 is not looking healthy.
Do tell us where you are. There are hardly any garden questions that can be answered without regard to location and climate.