You may not even need the nail caps. This kitten is so young, that training him to a scratching post should be a snap...in which case, you may never have destructive scratching behavior. Trimming his nails (very carefully at this age...I usually wait until 9 or 10 weeks to start) should be easy too, since he's a kitten. Be gentle, and move quickly. He'll grow to be a cat that won't mind this too much. If you do want to try the Soft Paws nail caps, I know that Petco carried them...get them in the tiniest size for young kittens...they come in funky colors!!!
Cows milk is a big no-no...most cats and kittens are lactose intolerant. Begin introducing solid foods by mixing KMR (Kitten Replacement Milk...you can get cans at Wal-Mart) with a good wet kitten food. Warm it up just a touch...usually microwaving it for about 8 seconds, and this is sufficient. I use Nutro Natural Choice Kitten Formula for 10 week-old Steuben. A 6-7 week old kitten will need to be offered about 5 small meals a day. When Steub was this little, I fed him at 7 and 11 in the morning, and 2:00 and 6:00 in the afternoon. He's also get a meal at around 10:30, before I went off to bed. By 8 weeks, I "weaned" him off the KMR, and just offered wet. By 9 weeks, I began mixing about a tablespoon of dry kitten kibble with his wet food, and that went well too. Now, at almost 11 weeks, he gets a can of wet food a day...1/2 in the a.m., and 1/2 in the p.m., and I offer a bowl of dry food to tide him over in between those meals. It's going great!
At 6-7 weeks, he should really not have too much problem using the litter box...just watch him to make sure he's doing so independently, and not struggling. Check his stools to see that they're well-formed and firm.
As far as other pets are concerned, the kitten should really have his own space for quite a while. Don't even think of letting kitten NEAR big cat until he's been given a clean bill of health from the vet. Once you know he's healthy and is not carrying any infectious diseases or parasites, you may begin the introduction process to you adult cat. First of all, never let your adult think you're favoring the kitten. If anything, the adult should have much much more attention bestowed upon him than the kitten...remember, you are officially the adult cat's property!!! Don't give him the idea that some little rug-rat can come in and steal the limelight!!!! I would bring the kitten out in the room where the adult is at the moment, and hold kitten on your lap. Big kitty may or may not want to investigate. If he does, let him sniff, hiss, growl, lick, etc., with kitten on your lap. No combat should happen...he big kitty swats or tries to nip, remove kitten, and put him back in his safe room immediately. Then go back to adult kitty, and shower with affection. Continue the lap routine for a few days, gradually increasing the amount of time, if possible. Next, kitten may be ready for a very short floor session with big kitty. This is where things could quickly get ugly, and if any combat ensues, remove kitten immediately. Gradually increase time, if possible. Also, know the difference between play aggression, and UGLY. Adults will hiss, growl, pounce, chase, and appear to bat the kitten around, and may look like he's swatting and nipping rather roughly. This may be play, and it may be ugly...you'll quickly be able to tell the difference.