I connected my scanner and found out that the fuel system is going into "closed loop" at ECT temp of 48 degrees.
I'm not quite following this, are you thinking that 48 degrees is too cold? Once started, the engine should operate in a rich state in open loop mode, until it senses a certain temperature, then go into closed loop mode where it operates leaner. If 48 degrees is that temperature (which I don't know), what problem would be indicated by this, by going into closed loop at that point?
What is the ECT temp sensor reading when the engine is cold and having trouble starting? I mean does it appear to be roughly what the ambient air temperature is? It's going to be in open loop mode when initially started and idling cold.
Possibly your thermostat needs replaced for other reasons, but that would be if it's stuck open and the engine takes a long time to get to closed loop mode due to that (which means it wastes fuel running rich and the heater takes forever to warm the cabin), or if the t-stat is stuck closed, and the engine overheats, but neither should cause it to run rough. I mean eventually, sure, an overheating engine can cause damage and the result is running rough, but nothing stated so far suggests that cause.
Excessive cranking when cold starting sometimes, Idles a little rough (fluctuates), At low speeds you can feel occasional miss.
Nothing in the original post was necessarily a problem to act on. THIS on the other hand, is.
Did it progressively get worse or all of a sudden? Could it be old or bad gas?
How old are the spark plugs and wires? Battery good and electrical system keeping voltage around 14V running? Does it crank to start at normal speed? Does it start a lot better when ambient air temp isn't very low?
Is the check engine light coming on, any trouble codes set?
You mentioned closed loop, does it get worse once it goes into closed loop? If so then you might have a vac leak. Does your scan tool allow realtime data to look at long term fuel trims while running?
Is there any pattern to when it idles rough, like does it happen when the A/C compressor comes on? If so then your IAC valve may be faulty or dirty/sticking, or A/C compressor failing. However that shouldn't be noticeable once driving, if it still manages to idle. Just wondering if it could be an accumulation of factors.