The phb says that you use your action to try and escape a grapple. The grappled condition says that it ends if the grappled creature is removed from the grappler’s reach. The phb also says that you can use an attack to attempt to shove a creature 5 feet away from you.
Can you grapple someone grappling you?
Grappling a grappler is fine and even the grappled creature can do it. If a nongrappled PC grappled a grappler of an ally and then dragged the grappler away from the ally, this would break the grapple on the ally. I hope that is less confusing then it seems.
Can you attack the target of a grapple?
Yes. We could dig into the grapple rules (PHB p.195) to show it’s so, but I think there’s an easier place to see it: the Grappler feat (PHB p.167). You have advantage on attack rolls against a creature you are grappling. Clearly, then, one can attack the target of a grapple.
Do you have to drop weapons to use grappling?
No. Grappling is an exceedingly rare maneuver for a reason. In order to use it, you must drop one of your weapons or a two-handed grip, reducing your damage potential. The debuff is pathetically weak, not even imposing disadvantage on attacks or anything.
Can You grapple a creature with an improvised weapon?
However, you may attempt to grapple a creature as a bonus action after hitting with an unarmed attack or improvised weapon. That can be pretty good! If your DM allows for ways for Improvised Weapons to become magical (such as a pair of gloves that give any improvised weapon a +1), then you can make this build work.
Can you use a grapple or shove as an opportunity attack?
It lines up with the fact that, if you get multiple attacks with one Attack action, you can replace one of your attacks with a Grapple or Shove. I don’t understand the intention behind not allowing Grapple or Shove as an Opportunity Attack. It gives a really nice crowd control option for melee characters that doesn’t require the Sentinel feat.