So what's the answer to Abathur? Because aside from just 5 manning a lane from the start I don't see a way around him fucking up all the early solo/duo lanes completely. There's just no winning any kind of 1v1/2v2 action against an Abathur team, and in solo games that's all you're gonna be getting for the first ~15 minutes.
There are quite a few ways to deal with him. I'll deal with your specific gripes.
First off unless you can outright burst the character 1v1 is out the door pre-10 with an Abathur on the field. His skill shot does too much and his shield protects too much. You simply will not win the fight. So don't pick them. This is a similar situation with if the opponents have a Brightwing on the field.
You need to know Abathur's symbiote isn't on an instant cooldown. It has a 4 second CD which is pretty hefty in a fast paced game like this. So while you are in lane always, always attack the minion that has the Abathur symbiote ontop of it. Furthermore the ONLY way Abathur can gain XP is if the kill occurs when he is symbioted on a near-by minion or hero. So a locust killing things or a toxic nest killing something
does not give XP. Honestly not even most Abathur players know this. So a good way to deny XP to the team is to simply refuse to let Abathur's symbiote live to leech XP.
You can have Nova try and pick him off or make him constantly move around. Remember forts & keeps do not grant true sight in this game. Only the core does. So if Abathur is in a spot where Nova can simply burst him down he's a free kill and she just walks away after taking a few tower shots.
Post-10 the only real benefit Abathur gives to the team is split pushing and his Ultimate. He still has good map presence assuming he keeps up with planting nests throughout the map but his Symbiote's damage starts to tail off in significance and if a 5v5 teamfight breaks out he simply has to use Clone. So you can somewhat exploit this by forcing clone, backing up then engaging again after clone goes away. Also remember Abathur's clone gains none of the talents of the person he is cloning so really it is mostly just a walking Ultimate.
Post-16 when Abathur gets Locust Nest this is generally when he becomes more active on the map. Try and figure out where you think he'll go (or if he's a bad Abathur figure out where he already is) and just go kill him. 9/10 the Abathur will Z to a pushed lane, spawn a nest and B home. So try and watch for that and if he gets predictable just kill him. This is also true for objective based maps and far sooner in the game. A good Abathur will hide in the bushes inside XP range of minions that naturally kill one another then also Symbiote onto a different lane to get XP from two lanes as once while you're focused elsewhere on the map. In general just look for where his locusts are coming from and that will be a tell for where he's at to punish this greedy XP soak.
