fix: address eighth round of PR review comments

- Complete incomplete sentence in fetch-profile guide
- Fix undefined castReplyingToAUrl → cast in messages guide
- Remove unimported Hex type annotation in messages guide
- Fix "th example" → "the example" typo in casts guide

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: rishavmukherji

src/app/(docs)/developers/guides/querying/fetch-profile/page.mdx

@@ -6,7 +6,7 @@
 
 </Callout>
 
-To fetch profile details, use the
+To fetch profile details, use the `userDataByFid` endpoint:
 
 ```bash
 $ curl http://localhost:3381/v1/userDataByFid\?fid\=1 | jq ".messages[].data.userDataBody"

src/app/(docs)/developers/guides/writing/casts/page.mdx

@@ -83,7 +83,7 @@ const castWithEmojiAndMentions = await makeCastAdd(
 
 A cast can be a reply to another cast, URL or NFT. A reply to another cast is treated as a thread, while a reply to a URL or NFT can be treated as a comment or a [channel](#channels).
 
-The optional parentUrl property can be set to a URL or to an fid-hash value of the cast being replied to, as shown in th example below. See [FIP-2](https://github.com/farcasterxyz/protocol/discussions/71) for more details on reply types.
+The optional parentUrl property can be set to a URL or to an fid-hash value of the cast being replied to, as shown in the example below. See [FIP-2](https://github.com/farcasterxyz/protocol/discussions/71) for more details on reply types.
 
 ```typescript
 /**

src/app/(docs)/developers/guides/writing/messages/page.mdx

@@ -25,7 +25,7 @@ import {
   FarcasterNetwork,
 } from '@farcaster/hub-nodejs';
 
-const ACCOUNT_PRIVATE_KEY: Hex = '0x...'; // Your account key's private key
+const ACCOUNT_PRIVATE_KEY = '0x...'; // Your account key's private key
 const FID = 123; // Your fid
 const FC_NETWORK = FarcasterNetwork.MAINNET;
 const ed25519Signer = new NobleEd25519Signer(ACCOUNT_PRIVATE_KEY);
@@ -60,7 +60,7 @@ A cast can be removed by issuing a CastRemove message with the hash of the CastA
 ```typescript
 const castRemove = await makeCastRemove(
   {
-    targetHash: castReplyingToAUrl._unsafeUnwrap().hash,
+    targetHash: cast._unsafeUnwrap().hash,
   },
   dataOptions,
   ed25519Signer