Loud clattering noise on cold start, only sometimes

[iTsYaBoiii]

Hello,

I recently bought a Lexus CT 200h 2011. 
The first couple of months went by mostly without a hitch, however, more recently I noticed a few worrying things.

Firstly, I noticed that very occasionally (not always) I get a bit of a shudder from the engine on a cold start.
This goes away within a minute or two. I did some reading and found that this may be due to one of a few issues - EGR valve having too much carbon buildup, bad sparkplugs or leaking head gasket.

Secondly, and more worryingly, sometimes on a cold start (not on every cold start) I get a rather loud clattering noise that lasts around 1-2 seconds and then goes away.
I am not really sure what this is, though again, from some reading I have done, it seems like it could be an issue with either the timing chain or the timing chain tensioner (though if that were the case I would expect issues on every cold start?).

Lastly, I also noticed a light misting of oil on the left back side of the engine (closer to the windshield on the drivers side), could anyone tell me what is located there and is it maybe related to the issues I am experiencing?

With the weather getting colder this past week, my initial suspicion was that this may be temperature-related, though I cannot 100% confirm it.
I have replaced the oil and oil filter just 1000 miles ago and replaced the spark plugs last weekend and both of these issues still persist.
I have also marked the coolant level on the coolant tank to see if it will lower over time in hopes of confirming if its a head gasket issue, though that hasn't produced any results yet (marked it last weekend and the level is still the same).


Realistically I am looking for some more concrete information on what the issues are and where should I start when it comes to repairs.

I am not a mechanic, however am capable of doing some repairs (have been servicing my Corolla before this CT 200h for 5 years, done brake pads/discs, oil, filters, brake hoses, brake pipe, sparkplugs...)
If this is beyond my expertise I would give it away to a mechanic, but would like to leave that as a last resort as I have been burned multiple times by them (misdiagnosis, ridiculous charges, poor work(didn't grease caliper pins which LED to my caliper locking up)).