Grappling, or being grappled, have no effects on attacks whatsoever. The attacker would carry out his attack as if the target were completely unimpeded, unless other conditions come into play (for example, the grappler proning the grappled target).
Can you attack while restrained?
The restrained condition in 5e doesn’t prohibit any action besides movement over space. So you can cast any spell while restrained. A “bound” creature cannot cast spells requiring somatic parts, cannot make attacks.
Can you attack again after having grappled an opponent?
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.
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.
How tall does an opponent have to be to get up after a grapple?
Attacks made against them from further than 5 ft have disadvantage. Being prone, they can get up with half their movement, except… So assuming you can grab ’em and knock ’em to the floor (which, yes, would be 2 attacks), they have to escape your grapple or they’re well and truly hosed.
Is it disadvantage to attack while grappled in RuneScape?
It is not a full nelson. Being prone does impose disadvantage on attacks, and you can’t get up while your movement is 0, so a grapple pins you. It seems like with another successful grapple check you could advance it to the prone condition which confers the same benefits except for the dis on Dex.