[RPG] Grappling hooks: how do they work

To the first question. Yes, "If you're able to make multiple attacks with the Attack action, this attack replaces one of them." (PHB 195) So yes you can attack again if you grapple with your first action. You are not limited to whom you attack, so anyone in reach including the grappled opponent is fine.

Your opponent is only frozen in place. That is the only restriction. He can attack you or anyone else if they are within his reach.

Advantage and Disadvantage work as normal, but nothing special is added due to the grapple.

There are not grappling specific attacks at this time, unless you have a specific spell or class feature that grants them. For instance the Grappler feat adds additional things to do with the Grappled condition, such as adding restrained.

So basically, as a part of your attack action, you can grab someone, all this does is set their speed to 0. That's pretty much it. There are other things you can do, but it's largely dependent on having class features or feats to support it. The WOTC forums have a lot more information in the Grappler's Guide that Ruut pointed to in his answer.

I think SevenSidedDie's response covers the basics pretty well.

On the specific question asked, if I where the GM, my ruling for this action would be (I am considering L1-4 characters):

1. Make an Intelligence ability check DC 13 during a short rest.
2. Spend 2d6 G worth of materials.
3. On a success, creates 1 explosive arrow. It must be fired within 1 day or it looses its effect as the components dry up. You can create and safely transport a number of arrows at a time equal to your Intelligence modifier.
4. Upon attacking with the arrow, the target and every creature within 5 ft makes a Dexterity save DC = 8 + Int modifier. Each creature that fails takes d10 fire damage, or half damage on a success.

Aside from following the mental process described by SevenSidedDice, I made these specific choices along the path:

1. The effect is kind of in the same tier as a level 1 spell.
2. The material cost and expiration date on the arrows ensures that casters with a similar effect are not overshadowed by it. The 2d6 is just a ballpark estimation, could be too much or too little depending on your style of play.
3. For more potent explosive effect I would add a higher DC to the crafting and much higher cost, but try to limit the damage and effect to something appropriate to the level of the characters.