Relating to first query,
No, you do not have to run your individual node. What I do know is blockstream esplora gives public API with documentation you may work with.
Relating to second query,
It depends upon what sort of segwit deal with(p2wpkh, p2wsh, p2tr) it’s, however I assume what you need to spend could be the commonest segwit transaction, which is p2wpkh(single signature with public key).
For p2wpkh segwit spend, you may refer beneath code working for nodejs, which you will discover right here, too.
import * as bitcoin from 'bitcoin-sdk-js';
const privkey =
'e6c58327b4bf1314296bba7adb66f94c36ea5611ac07830c229aa7ee6f9caac3';
const toAddress="tb1qmjqyknun9umlwlle5nuy8jz9ms7v85cp7k2nfe";
const toValue = 300000; // unit is satoshi
const txHash="8bcd197873dbff5cc67cb3e0b1cbbdf097c7af94b0e9365adecb424e408294bf";
const inputValue = 310981; // payment is enter worth - whole worth
const tx = new bitcoin.Transaction();
await tx.addInput({
txHash: txHash,
index: n, // it ought to be vout of utxo, index of utxo in transation
worth: inputValue,
});
await tx.addOutput({
deal with: toAddress,
worth: toValue,
});
await tx.signInput(privkey, 0);
const txHex = await tx.getSignedHex();
For different kind of segwit deal with, it actually varies on unlocking script, so there’s probably not a technique resolution for it.

