First of all, I hope this is in the correct section of forums. Looking at the previous threads it is. :P

Moving to the point, Shen is by far my favorite tank champion. I know he doesn't really have a place in the meta / comp game due to how much gold he needs to succeed, but I usually play in a solo queue anyway (at least for now, only Level 23).

Due to only being Level 23, my mastery is not fully complete, but it is currently 9-14-0.

I took attack damage (Brute Force), summoner spells improvements, cooldown reduction (sorcery), and magic penetration (arcane knowledge).

Then the (start) of the generic tank defense tree.

Again, due to Level 23 my rune page is not complete (I also need a new rune page just for Shen), but I use magic penetration marks, armor seals, magic resist per level glyphs, and attack damage quintessences (will be replaced, only ones I have right now)).

As for my actual in-game build, I choose flash and exhaust for my spells.
I typically start with boots + health potions.

First trip back I upgrade my boots into mercury's treads and start building my sunfire cape (sometimes buying more health potions / wards as well).

My late game build usually looks like:
Mercury's Treads, Sunfire Cape, Aegis of Legion, Randuin's Omen, Banshee's Veil, and Frozen Mallet (assuming the game goes on long enough).

Is this a viable build for Shen?

He has plenty of place in the current meta.

Shen functions well in 3 of the 5 positions.
He's strongest in solo top right now. He's still one of the best solo tops due to his early game burst and sustain.

Shen is also an excellent jungler. Being independent of mana means he can start red or blue and feed blue to your mid. Starting red also means that you can perform level 2 ganks with your amazing gap closer+CC. He's also incredibly safe in the jungle as he can dash through walls to run away, as well as duel effectively with his abilities.

Lastly, he can technically be a support in bottom lane with his vorpal blade granting healing and zoning opponents with his dash and poking with vorpal. He's not the best at this, but it's certainly viable.

As for your builds:
I recommend changing your Marks to Attack Speed if you go anywhere except for bottom. AS runes means more frequent Ki-strikes, and it's important to his late game damage. Armor and MR are also good picks. I don't think AD is the best choice for him. Personally, I run MS, but you can try HP quints as well.

I recommend avoiding Sunfire. Yes, it's great HP and armor as well as some damage on the passive. But IMO it doesn't do enough. I suggest rushing a Phage instead (eventually turning it into a mallet). The HP and sustained slow will help you become better at peeling as well as add to your damage and survivability. You should also look into Atma's Impailer and Wit's End as other items.

I usually jungle with him so my summoners are Smite/Ghost.
My build is variable since he's such a stable jungler.
I can start Doran's Shield, Doran's Blade, or Boots+3 pots (no need for the armor+5 really, I want offense because I gank early and often).
I try to rush a phage and a giant's belt, then look into armor and MR items.
Probably just get a chain vest and Recurve bow. Look into upgrading to Wit's End and Atma's. Also look into getting more defense later on.

End game usually looks like this:
Merc Treads
Frozen Mallet
Wit's End
Atma's Impailer
Randuin's
Force of Nature

If I need more damage late game, I sell Wit's End and build Madred's bloodrazor. FoN and Merc Treads is sufficient MR.

Yes, I know I'm ignoring Warmogs. I don't like Warmogs. but I suppose I could get warmogs instead of FoN if I keep Wit's End, but it feels late in the game to do that.

Shen needs gold to be successful? If you mean he needs gold to do HP damage, then sure, but without gold he's still got great initiation, CC, durability...

If you're going against a low AP team and/or if your mid dominates their AP carry early, then instead of Wit's End you could grab an Ionic Spark. Same attack speed boost, slightly less damage, better farming, and a bit more HP instead of MR. You need to be certain you can get away with it, though, because the MR on Wit's End will help way more than the slight increase in HP if their team is doing a lot of magic damage.