i'm going to be a bit more brutal with my comments but you have asked for more tips or comments
the first of the second two photo's posted although it's in focus and well exposed the pose looks awkward and the eye is dead ( no catchlight ) unfortunatly it makes the photo not very interesting
there is a "classic pose" that you will see in most photo's of nuthatches but it's not the only pose that works but it is the preferable pose so to speak
something like this
this is an image i have posted previously so you might have seen it allready but it gives you an idea of what i'm talking about when i say "classic pose"
i think a catchlight in the eye of most birds is reasonably important without one the eye looks dead and unfortunatly is not a keeper
on a positive side the background is nice and clean the nuthatch is well exposed and the focus is spot on there's nothing wrong with how the photograph was taken
if i was to show you some of my very first photo's of a nuthatch there a lot like yours in fact there worse
i was just happy to get the bird in frame but after a lot of photo's and a considerable amount of time photographing them i tend to wait for a pose i am happy with but even then my photo's are not perfect and i'm allways striving for that better shot
on to the second photo...
to be honest it doesnt work for me
too much in shadow but not a shiloette it looks like your camera has exposed for the background rather than the subject i would be tempted to set the camera manually and go up a stop to try and keep the subject exposed properly
i know this isn't the photo critique thread but you are asking for advice and just posting " lovely photo " tells you nothing about what might be improved hopefully you won't take this the wrong way and you understand it is only my opinion
it's worth finding a nice branch that you can put near the food making sure the background is clean where you decide to place the branch, it will land on the branch along with whatever else comes to feed
all there is to do then is wait for a pose you are happy with
bit like fishing in a sense.......
EDIT...
while i was writing this matt ad posted "lovely" i hope you don't think i was directing my post at anybody in particular it is just something i see in a lot of posts and there's nothing wrong with that but the OP is asking for some advice / tips