Greatly overtuned numbers but those are variable.
Being melee significantly changes the core of the champ. Vlad is an aristocratic hemomancer, not a bloodthirsty ravaging vampire beast. Would be better served as a new champ. The remake wont happen like this anyway so we can ignore this factor and critique the kit itself.
The scaling off health is really razor's edge. You gain tons of survivability in addition to damage. Ryze can stack mana because its useless unless you need more of it to cast. Health scaling abilities have historically had terrible coefficients because health is such a good stat anyway. Who doesnt want more health (magic star unigoatcorns excluded)
Passive is far too powerful and even more "toxic" than his current passive. Veigar and Nasus have a specific paradigm to stack their passives. This one is far too powerful, adds no gameplay. To be balanced it would have to be toned down including the rest of the scaling to the point of just feeling bad.
The stealing of max health is an iffy thing. Could work if done right but runs into issues. Does the increase grant an equal amount of "current HP" to the increased "max HP" (basically healing like Nasus, Renek, and Gnar). Or does it just give a empty increase. The latter would work with vlad considering his self healing abilities. Number tuning may be hard since a single ability granting 600HP is usually reserved for temporary ults or hungry void behemoths. The healing for a percent instead of a seperate scaling value (thats currently in place) adds a few problems. Using it on a high resistance target will give pitiful healing, while using it on a squishy will give a huge disproportionate amount of health. A super HP tank vlad would already be hard to kill for a squishy damage dealer, let alone if vlad gets more healing from them than other champs.
Pool - The movespeed is needed for a Melee champ with no other gap closers. Is basically unavoidable damage because you cant run away from it, when before you could unless you were already in it. HP damage scaling is redic but already covered that.
Tides - The one I have the most issue with. The CD would prob be greatly increased but still. 5-8 seconds for the debuff is forever in LoL terms. Also unavoidable PB-AoE for such a powerful skill. Turns vlad into a AP auto attacker with basically the best ratio this side of emperor sand birds. The damage increase may nessecitate all his other spells being nerfed to compensate, making them hit like wet noodles UNLESS hit by this spell. OK for Swain with his long CDs, but with vlads massive sustained auto attack damage seems questionable. Also grants Vlad a perma slow. The same thing keeping old skarner from being buffed properly. Excessive stickiness without proper counter play (all his skills are targeted) isnt the best game play. Overloaded ability.
Ult - This one is just ridiculous. The numbers on that thing is just unbelievable, but again already mentioned. A second move speed increase. You cant out run from the blood. Kennen has to use his one movespeed skill to position his PB-AoE ult. The scaling is so redic I have to mention it again. It hits 5-10-15 +10x? times for 0.5ap + 2/3/4% max HP each. Rank 3 with no stacks of flurry has a 5.0 +40% targets max HP ratio.
Overall this vlad incarnation will end up being an super massive HP tank with some AP. He gets FAR too much damage for building to be unkillable while also being a lifesteal tank. Minions give him the most healing, allowing him to shrug off harrass. Oddly even though hes AP, Atmas (rip) would probably be viable considering his auto attacking. HP steroid and some HP items with some resistances thrown in makes a huge tank while doing damage based on his tankiness. Both because he scales hard of HP, but because of his persistent damage nature. If he gets on you, he perma slows you while doing very high consistant undodgable damage thats ALSO based on your own HP. Hes a giant meatshield that cannot be ignored. Rylias would be core, adding to his annoyingness.