I would like to install a whole home water filter just after the water tank. The line coming out of the tank to the rest of the house is 3/4in pex. The filter systems that I have looked at so far are all 1/2in connectors. If I use 3/4 to 1/2 adapter to connect to the filter, then another from the filter back to the rest of the pipe system, is this going to cause any negative affects to the water pressure for the rest of the house?
I would have to question your reasoning for filtering all the water you use in your house. Filtering can get expensive when you start having to replace filter cartridges, especially those rated to take most of the nasty things out of the water. It really is a waste in most cases to be using filtered water to flush toilets, wash cloths, shower and wash dishes.
It is a lot more cost effective to install a filter at one location, such as at the kitchen sink, where water is filtered to a separate valve for drinking, cooking and to feed the ice maker in the refrigerator.
If your reasoning is based upon hard water that has a lot of dissolved minerals or iron in it then there may be better choices to use a water softener rather than a filter.
No. short lengths of slightly narrower ID pipe will not have any noticeable impact on pressure.