Shen just doesn't do much. Look at his spells and just compare them to other champions and just at his abilities:

Passive: bonus damage every 8 seconds. Actually a decent amount of damage, but the hp scaling runs counter to everything else he does.

Q: Compare to Akali. If Akali gets the onhit effect her Q does better base damage but scales worse, although it has longer range. It costs quite a deal less though. If she doesn't get the onhit it costs more and deals less damage, but still has a higher range.

If you want Shen to build AP this could be okay, although the heal is too weak right now and his energy costs are way too high, prohibiting sustained usage. The heal needs to scale or be replaced because it doesn't have a strong effect. If Shen isn't supposed to build AP then this spell is too weak. It has a tiny range, a prohibitive cost if trying to use his other abilities, and doesn't do much base damage.

W: A shield. Nothing special. This could be pretty cool though, so let's look at Riven's shield to compare. First, Riven has a 1 second longer cooldown but gets a short dash. Her shield scales better (.25 more scaling - sure the stat is less available but it is more generally useful as well.) Shen has the benefit of 70 extra base shield and 1 second on his cooldown, at the cost of 45 energy, no dash, and .25 scaling.

If you compare it to Veigar's Q (a basic ability that is almost pure nuke) it does less base damage, has a longer cooldown, but does admittedly scale better. If AP is a stat that Shen wants it could be slightly stronger, although remember that Q-farming will increase Veigar's damage.

Ultimately this ability seems just a little bit too weak if Shen really wants to itemize AP, and waaay too weak otherwise. I think it either needs some rather large number tweaks or some conceptual changes.

E: This spell is pretty cool. You get a short dash and taunt people. The dash range makes sense - comparing the range to Riven's E's range the range is similarly cooldown efficient. A lower cooldown is better in general and Shen's range is a little more efficient, so that is alright. Looking at the taunt, it is similar to Rammus's taunt. Rammus has a 1 second and armor reduction benefit, but a longer cooldown and no dash/slightly less range. The taunt is nice as a 2 second cc, although it doesn't seem very "tauntish" seeing as you can't really move the target much and won't be taking very much damage over just two seconds.

Finally, it has a huge energy cost. You need 100 energy to use this, so it takes a while or not casting if you were at full. You can't spam his Q and W and still end up being able to cast his E. He uses both abilities too - Q has a small heal and is his only real damage while W helps him be a tank. This ability is cool but the energy cost takes away a lot of its usefulness.

R: The concept is pretty cool. In a full blown teamfight this is just a damage shield on your carry or someone and is only really useful as damage control. It won't be good unless things go badly, in which case it's useful for delaying things. This is great for assisting in small fights though and makes any 1v1 into a 2v1. The shield and scaling is just silly.

In conclusion: Shen is a tank - his skills all point to that (teleporting to an ally, shielding yourself, taunt, and no huge damage abilities.) However he can't be itemize to take advantage of his kit. If you build AP he doesn't have the resistances or health to tank and doesn't do enough damage to justify his presence. If he builds tanky his Q and W are rather negligible and he is left with a shield and a taunt. If he itemizes health he can get large atma's AD and large passive triggers but doesn't tank very well and his abilities are weak. I think the biggest thing I would do is try to change his itemization a bit.

His Q needs scaling on that heal - I would make it be something like heals 50+.2 AP to allies and 75+.35 to self (numbers are pretty rough). I would have it heal you more so I can make the heal important for Shen but not too strong when healing allies.

His W could give armor/MR, either passively or as an active. Right now you can't have a meaningful shield and good resistances, this change would alleviate that and allow you to build AP while not falling too far behind on defense. Probably a passive MR/armor and a larger bonus when active.

For his E I would reduce the cost to something like 75 restoring around 40-50 energy for a champion hit. This way you can use it to run away but you can't spam everything, or you can use it offensively and spam your stuff.

On Shen's R I would probably not change much. If anything it might need a bit of a nerf, although I'm not sure. Quite possibly a cooldown reduction but a nerf to the shield amount.

The passive. Right now it kind of sucks and he is shoehorned into AP with the rest of my ideas. Making Shen scale off of health would bad - there would be no reason for him to get armor/mr so his W would have to give him all he needs. Since there are no +armor AP items it would be good to give him armor somehow. Maybe a system where Shen gains bonus armor/MR (less MR) whenever he hasn't been hit and it stacks. Every time Shen is hit by a champion he loses one stack. This way he prefers to fight small engagements where he is hit less and it gives more incentive for short fights. He can use w to avoid most of the damage and get away before he loses all of his bonus armor/MR. This would give a nice dynamic where Shen helps his team split push and otherwise fight small engagements. His heal, W, passive, and R are all much more useful the smaller the engagement. (His E is just always useful in engagements.) The way to deal with Shen then would be to force a full teamfight. That is where he would be the weakest.