Bought a 20 year old house last spring and it appears to be settling - when to call in experts
None of the pictures in your question necessarily point at a foundation issue.  You have cracks in your drywall.  

What could cause these?


The first picture is a screw or nail that wasn't set in the drywall properly.  This means nothing.
The other pictures could be poor drywall techniques.  You just bought the house so you never lived through a winter.  This house could have had these issues for 20 years and they just did a quick cover up before selling.
Another thing is the humidity levels in your house.  Maybe the previous owners managed these things better.  Sharp increases and decreases in humidity levels will give drywall fits - especially improperly installed.
And what I would most likely be concerned about before a foundation issue is the amount insulation in your basement.   Your cracks in the basement are right where most air comes into basements without proper insulation and air blockage.
It could be that you had an unusually wet/dry/hot/cold season.  These things will happen because houses are made out of wood framing.  They are less likely to happen if you are in Europe and your house is made of insulated cinders.


What would I do?


Investigate the foundation.  Take some pictures of any issues that you see.  Look in and out of the house.  
Make sure the buildup of dirt around your house is proper for drainage.  If there is a foundation issue after this many years it is probably it is caused by improper drainage next to the house.  Investigate any depressions in the ground that could be caused by animals, poor draining gutters or poor maintenance.
Investigate the wall of the basement.  You might have to take out some bits of drywall in a couple of places.  It is a bit messy but cost is very low.  Look to see how it was insulated and if there are any water issues.
In the end I would screw the screw in all the way and hit it with some mud and repaint.  The cracks I would caulk, then mud/tape/repaint.  I would be done in an hour and it would cost $20.


If you want to hire a foundation specialist in my opinion it is overboard.  Probably a better and cheaper solution would be to hire a different home inspector that you used when you bought the home - in my opinion this is overboard too but offering a better solution than having an engineer come out.  If you need an engineer the home inspector can point you to the right person.

Note to OP:  If this is your main concern after a year of being in a new house, then you probably got a pretty good house.  Chill on the engineer.  Know that things like this happen because wood expands and contracts.  If it freaks you out drink more or read up on how to keep your house at a more constant temperature and humidity level.