What was given to Scout when she wasn't looking while standing in front of the Radley place? And what did Nathan Radley do to the tree in his yard that Jem and Scout found things in? What was his reason for it?
While Scout stands in front of the Radley place watching Miss Maudie's house burn, a blanket is placed around her shoulders without her noticing. Atticus is initially disappointed that she did not stay put as he asked her to, but when he sees her confusion, he realizes that the blanket has been placed around her shoulders without her knowledge—probably by Arthur Radley, given their proximity to the Radley house and Nathan's preoccupation with helping to put out the fire. When a frantic Jem says that they can't publicly return the blanket for fear of getting Boo in trouble with Nathan and explains about the knothole, Atticus agrees that they had better keep the gift of the blanket secret. Scout feels distinctly ill at the thought of Boo Radley standing right behind her without her knowledge.
Boo Radley leaves Scout and Jem little gifts in the knothole of the tree. It is his way of communicating with the two children and trying to be their friend. Ultimately his friendship is made clear when he shows up in person when he saves Scout and Jem from Mr. Ewell's attack. The items that Boo Radley leaves in the knothole are as follows.
1. 2 pieces of chewing gum. Jem did make Scout spit it out, because he was suspicious.
2. 2 scrubbed and polished pennies. Jem confirmed them both to be rare Indian Head pennies from 1906 and 1900.
3. A single ball of gray twine.
4. 2 miniature carvings of Scout and Jem made out of soap.
5. An entire package of chewing gum, not just two sticks.
6. A spelling bee medal.
7. A pocket watch.
Nathan Radley is Boo's older brother. He stops Boo from placing gifts in the tree by plugging up the hole. No reason is stated as to why he does this. Nathan tells Scout and Jem it's because the tree is sick, but Atticus tells his children that the tree looks healthy to him. The reason is likely that Nathan wants to continue to isolate his brother from the public. If Boo is isolated, then he can't do anything that would get him in trouble. It sounds very controlling, which it is, but there still is the possibility that Nathan truly believes that he is protecting his little brother.