Codes P1805, P0102, P0113 and Engine rattles?

Yes the poo11 code is the most important one in the list especially if the engine has a rattle. It indicats a problem with the vvt variable valve timing. It usually means that the vvt oil control solinoid might be broken might be time to replace it. The parts pretty cheap. Also. As a side note it's not good to drive the car till its fixed might damage somthing. But the rattle should go away and it should run smooth again once the problems is solved. Also the po102 code is a maf sensor and the po113 code is a ait". Or intake air tempsensor code. These two somtimes go away after vvt problem is fixed so fix it first clear the code and keep an eye on it for a while. Good luck

It looks like you have two or three problems, the first is the MAF sensor needs to be replaced, or you have a crack or the air intake tube is disconnected between the MAF sensor and throttle body.

This guide can help:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

P1805 Brake Switch or Step Motor Circuit (often Transmission-related)
P0102 Mass Air Flow (MAF) Sensor Circuit Low Input
P0113 Intake Air Temperature (IAT) Sensor 1 Circuit High Input
P0011 Intake Valve Timing (VVT) Over-Advanced (Bank 1)

If the intake tube is good, I would replace the MAF sensor and then clear the codes, please start new threads for the P1805 and P0011 codes separately. Here is the sensor in question. Check out the images (below). Let us know how it goes.

Good find on the cranked intake tube, that will cause the:

P0102 Mass Air Flow (MAF) Sensor Circuit Low Input

Yep, I would put the engine on TDC before taking the engine apart unless the chain it not turning the camshafts, if this is so the engine will most likely need to come apart because of bent intake or exhaust valves. Can you upload images of the problem so I can be sure?

Yep, good find on the timing chain issue, I don't like hearing that the chain skips though, you could have bent valves, also can I ask which phone you used to upload the video? It does not work, and I want to tell the webmaster of the site. When you get the timing chain back together, crank the engine over to see if you have compression or not.

This guide can help:

https://www.2carpros.com/articles/how-to-test-engine-compression

Please go over this guide and get back to us.

New video format thanks. That is good news that the valves are okay. Here is how to time the engine crankshaft and camshafts. Check out the images (below). Let us know how it goes.

I don't understand what you mean by "I would have to force it"? Did the camshaft not bolt down fully?

Could it be the valves are contacting the pistons? Is the engine on TDC when you line up the camshaft marks?