First, what browser are you using? If it's IE, switch to Chrome or FF and that'll fix about half a dozen problems on its own and both of these problems may stem from using IE. If you aren't using IE (or even if you are) these may also fix your problems:
Make sure you're putting clothes on in the Wardrobe, not the Dream Builder (Dream Builder is just so you can plan what you want to get and what you want your avatar to look like). Also, save both in Body Features and in Wardrobe. Not sure why you have to save in both places for the changes to take, but you do.
How many tabs do you have open? Egg pickup sometimes messes up (often messes up) if you have more than one tab of Rescreatu open in an area where you can find eggs (NPC shops, planets, bank, etc). Also, make sure it's been less than 2 minutes since you found the egg, as the egg basically "expires" after 2 minutes and you can't pick it up (it only expires for pickup, it doesn't spoil for a week after it's picked up so don't worry about that speedy time limit).
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