For future reference it is hard to critique multiple shots in the same post because when we click the reply button to put in our two cents we don't have the picture in front of us. I personally find myself opening up the note pad program to jot down notes so i remember what to say about the photos. But here is my critique of what you posted.
First off I'll address the tilt most others have touched on. Your not doing anything wrong per say. Every shooter tilts to either the left or the right. You'll notice a lot of people that shoot buildings can never get a shot perfect in camera because our natural body mechanics skew fractions of an inch one way or another. If you were to measure your appendages on your body you would notice one side is larger then the other by fractional increments. one leg is slightly longer, one arm is slightly longer, one hand is slightly larger and this contributes to the slight lean in most shots. I would bet if you looked back at all your shots where you held the camera the same way (flash facing the same direction when you orient the camera) they would all probably have a slight tilt the same direction. It also doesnt help that the world isn't flat and our shoes flex to form to the earth below us. We don't notice when our eye is in the viewfinder but when you take a static frame and put it in the computer where everything is perfectly straight the grid shows you it's crooked. You can try to remedy this issue by training yourself to cheat the camera orientation the other way just a little but then you risk over correcting and making all your shots look worse then if you just use the corp grid, even if you don't crop the photo, so you can level out with the grid lines. I do this with my iphone by using the grid to try and level things out in camera but there is still a slight shift.
On to your photos:
1. The statue is cut off, as stated before. As well as the area around it. Either zoom in tighter on the angels face and use a wide open aperature to blur the background more or take 2 steps back as you did in #3 and get the surrounding area framed in and see the bottom portion of the statue. If you take multiple shots you can still tell the story of the church because in one shot you can show the art on the sealing, and the next shot you can blur everything but the angel looking at whatever it is looking at.
2. The leading lines work in this photo but the issue here is distracting elements within the frame. There is boring space to the left of the girl and empty pews to the right. These areas don't need to be in the shot. I think it should be zoomed in tighter to show more focus on her. If you think of a close up head and shoulders kind of composition that might get you where you want to be. Keeping that frame in the back of your head for next time you can focus on her face, ideally her expression through her prayer. People tend to talk to themselves or cry in prayer and that can show great emotion in a shot.
3. Pillar to the left is unneeded and distracting. Perhaps take 1 step forward to get tighter perspective and still incorporate the arch with the statue. If #1 and #3 had a baby it would be a really nice shot. Or you can tilt up so you incorporate the paintings on the cieling with the statue and the bottom of the frame would start at the statues belt. There is a member on here that shoots cars a lot and he wrote up a great article on "zooming with your feet" and it applies to more then just cars. Perspective is greatly effected by where you stand when you take the shot. You can zoom with your lens from for example 35mm to 50mm but that effects your depth of field and takes things away from the frame whereas if you took a step forward here and dropped to a knee and tilted the camera up it may give a better feel overall. I wasn't at the church with you when you took the shot but this is how I imagine taking the shot if I was there.
4. My favorite of this series. The exposure looks nice. Maybe tighten the aperature by half a stop (f8 instead of f7.1) to define the star from the sun a little more and add drama to the faint clouds. Composition looks good aside from the tilt that you can't avoid without practicing. Like shooting a rifle from a standing position. You won't hit the center of the target the first time but as you hold the weight of that rifle of and over and over without added support your grouping will get tighter and tighter as your muscles get used to the weight. Remember a camera is a lot like a rifle in that the shooters breathing and mechanics effect the outcome of the shot.
5. I think I see what you were going for but it didnt work here. Crop the 5 links that are around the flag so that is the only focus of the shot. The center hole(link) should have the flag in it as you have done. The sign to the right is not needed. Don't need that many bushes to the left either. I dislike the vignette. I think the flag should fill the center hole (link) so I agree with the other it should be bigger. Without holding the camera and trying to shoot the same shot I am unsure of how you would do it but hopefully this advice from everyone helps you when your out.
* A lot of these suggestions, as you said before, you don't really think about at the time fo taking the shot. I like to think none of us really go through the check list of "rules" when we take a shot. It's like getting into your car. You don't think to yourself I have to open the door, get in, put my seat belt on, close the door, take my keys out, put the right key in the ignition, turn the key, press down clutch/brake, shift into drive, GO. Once you exercise these steps over and over it's just something you do sub consciously. And by all means rules are there begging to be broken but if you go out for a shoot and think to yourself I'm going to examine what is in my frame. Do I really need that in there or should I zoom in some more, then your shots will generally get better with time. Same goes with shooting groups of people. Frame up the shot and before you activate the shutter you count faces and make sure you see a face for every body. Sounds crazy but I know a couple people that shoot a group picture and someones face is covered by uncle Jim's head or a leave or there is a beer can in the shot on the table where nobody was paying attention. How do you think celebrities get busted for drugs, because the person shooting the picture forgot to say move the bong out of the shot so there isn't evidence that we been SMOKIN!!! 
I hope this makes sense and helps you in further shots. I'm no expert because I'm still learning just like you but I do know how I would shoot those shots and try to explain one idea of how to do it next time. If you ever go back to the church I would love to see what you come back with the second time around. Chances are they will be better.
"A great photographer can take great shots with an Iphone but a mediocre photographer can ruin a shot with a 1dsmkIV. My camera is like the brush I paint a house with...I'm just looking for my detail brush, and a roller, and some high gloss paint, and a sprayer, yeah a sprayer would make things easier."
by LC8212
