First of all, remind your nephew that if you're the photographer you can't enjoy the wedding as a guest. By asking you to photograph his wedding, he's essentially uninviting you as a guest. I don't think many couples who ask a relative to be their official photographer realize that. I know you said he's on a budget, but if he can swing a professional photographer, even if it means only a few hours of coverage, he should try to go for that (at least for the ceremony and formals). They might want to reallocate money from the flowers, decorations, food for photography. Flowers die, food gets consumed quickly, and no one will remember or think about those things the next day, much less years from now, so don't spend more money than necessary on them unless you can afford it. Photographs are forever and will be cherished for generations to come, so it should be a priority. If that's out of the question, then here's my advice for you.
Make sure you have enough memory cards to last all day without deleting any of them. If you get an error on a card stop using it immediately, so you can maximize your chances of recovering the files later. Don't clear any of your memory cards until you have the images saved on at least two other drives/discs (computer's hard drive/external drive and DVD backups) and you have VERIFIED that those copies aren't corrupted. If you can, get a backup camera, lenses, and flash. Equipment goes down all the time, and as the official photographer there are NO excuses for not being able to continue shooting. I've had friends who had two professional cameras and flash units break down during a wedding; It was a good thing they had another camera body in their car or used a second shooter's camera. I can't tell you how many times I've had equipment go down on me -- lenses, flash units, camera bodies. If you can't swing for an extra DSLR, then at the very least bring along a point and shoot as a backup (last resort). Also bring extra batteries. Don't rely on RAW to save your images. RAW is wonderful, but it's not fool-proof.
Remember: THIS IS THE COUPLE'S DAY! Don't do anything that will distract attention from them and call undue attention to yourself. The most important and solemn part of the day is the ceremony, so absolutely do not under any conditions use flash in the church during the ceremony. I'll say it again DO NOT USE FLASH IN THE CHURCH DURING THE CEREMONY. It's annoying, unprofessional, and it disrupts the flow and mood of the event. Just because the couple is on a budget doesn't mean their ceremony doesn't deserve respect. Check with the priest to see what you can and can't do and where you are not allowed to be. Photographers often get kicked out of church ceremonies for being too distracting or for doing stupid stuff, like walking up by the altar to get shots. This is a wedding, for crying out loud...you wouldn't walk up on stage during a Broadway play, would you? Even when priests say that they're okay with flash, it's just not cool at all. The only time it's okay to use flash in a church is up until the bride completes her walk down the aisle. Once she reaches the altar stop using flash. You can use flash again when the official ceremony is over, they kiss, and the couple starts coming back up the aisle. (Flash is okay for outdoor ceremonies because it's only fill flash and it not really noticeable in the bright sunlight) Inside the church crank up your ISO. On your camera that may mean 1600 or 3200 (no higher than that). Get a long lens, and maybe a tripod, and take pictures from the back of the church during the ceremony. If you don't already have fast glass (max aperture of at least 2.8) rent some and open up that aperture in the dark church. Don't forget to change your settings when you leave the dark church into the bright outdoor light.
Get your formal shots done, if they want formal. It's easier to start with the largest group and work your way down to minimize moving people back and forth. This is often the most unpleasant part of the day. Work fast. Keep reminding the people who you are photographing that YOUR camera is the one they should be looking at, NOT the other 100 cameras that guests behind and all around you are using. Despite your constant reminder of this fact, expect lots of shots with people looking in other directions. This where experience helps. It's more than just taking nice pictures. It's consistently taking nice pictures in a split-second's notice, and controlling/directing masses of people without appearing to be rude. If your "keeper" rate of good photographs isn't high, then you shouldn't be photographing weddings. Don't shoot indiscriminately; anticipate and shoot at the right moment.
In your second question you mentioned a busy park. I assume that's where the reception will take place. Well, for shallow depth of field you'll want to use large apertures. Depending on distance to the subject and focal length, that could be f/4 or f/5.6 and larger (larger means the f-stop number is lower...so f/1.8 is larger than f/5.6 and would have shallower depth of field). Distance to subject also controls depth of field. Remember to focus on eyes. If the subject's eyes are in focus, it will be more acceptable if other parts are blurry. You didn't say what time of day the reception will be, but if it's in bright daylight, then a large aperture will necessitate very fast shutter speeds and low ISO. If you have mixed lighting, where subjects are in shade, the differences in light can be dramatic, and settings that work for subjects in bright light would cause drastic underexposure for a subject in shade. In fast-changing light the semi-automatic modes (aperture priority or shutter priority) can be your friend. Don't be afraid to get a creative with reception shots. While the bride is the star of the show, and you should always know where she is and what she's doing, remember to get lots of detail shots and guest expressions during the ceremony and the reception. Those shots really "tell the story" and years from now they will transport the couple back to their special day. The couple is often so busy during their wedding day that the photographer captures moments they couldn't see themselves. If you know that people the couple rarely see are present and came a great distance, make sure you get shots of them. Ditto for guests who may not be around for long (I know that sounds a little morbid, but the couple will be so grateful to have that shot of great grandma after she's gone). Don't forget to eat and stay hydrated, and wear comfortable shoes (a fresh pair of socks can feel like heaven part-way through the day). I know people who exercise regularly, yet they still feel like they were hit by a train after shooting a full wedding.
Finally, know that no matter what you tell the bride; no matter how low you try to set her expectations, saying that you're not a professional photographer, she WILL be disappointed if you don't deliver professional results. I hear it all the time when couples ask friends/relatives to shoot for them. They may not tell it to your face, because they don't want to hurt your feelings (but sometimes they do), but I hear the regrets all the time. People have even sued their free photographers because they were unsatisfied with the photography and can't re-live that moment in time. That's why pros carry indemnity insurance and always get contracts, even when they shoot for free. Weddings are draining and stressful. A high percentage of wedding photographers get burned out and stop shooting weddings. There are lots of pros who do portraiture and other types of photography who would never consider doing weddings because they're scared to death of them!
Have fun!
and my nephews upcoming wedding on October 10. The couple is young, and he is in the Army. They have put this wedding together quite fast, and on a tight budget. I have been nominated to take photos. Mind you, I am in NO WAY a photographer. I like to take photos. Some are great, some are not. I'm starting to feel the pressure. I know lighting in churches is usually funny at best. I have a decent understanding of composition, but can't recall it quickly and accurately enough to get great results.
(They were not going to hire a pro like I fully recommended).
, GrillMouster! If that doesn't scare people away from doing wedding photography, I don't know what will! 
