I have 2005 chrylsr 300 limited v6 engine and I noticed and now it is getting worse..that when I am at a stop and then I begin driving the car shakes and then it drives smoothly and then it shakes again while driving. What could this be?

google 2007 Hyundai azrea limited 3.8 v6 engine coolant temperature sensor location. You have other problems
copy and paste

https://www.youtube.com/watch?v=pFA02AckRAw

Question edited to add maker.

Chrysler 300 Transmission Fluid Capacity and ... - Engineswork

https://engineswork.com > oil-capacity > chrysler-300-t...
2005 2006 2007 2008 2009 2010 Chrysler 300 Transmission Fluid Capacity ; 4-speed 42RLE automatic transmission, Total Fill 8.3 liters (8.8 quarts) ; 5-speed NAG1 ...

2005 Chrysler 300 2 7L V6 Spark Plugs and Plenum Gasket Replace
this video about changing spark plugs and plenum gaskets on a 2005 Chrysler 300 2.7L v6 engine. I forgot to mention that you should change or clean out the PCV valve because it is almost impossible to get to when the plenum is on. You might also want to double check the torque specs for your own piece of mind, I torqued mine to 7 1/2 ft lbs. Make sure you get the metal egr tube in the back on correctly without tearing the rubber washer, it's tricky. You might want to take the egr tube off from the other end at the exhaust manifold so you don't bend it.

Sounds like you have a transmission pump issue,you will need to take it to a tranny shop to diagnose if that is the problem if in drive it does not whine.

find an accredited service shop and get a proper diagnosis done and a quote
the suggestion from the mechanic indicates a limited knowledge and the procedure to follow in testing and problem solving

A blockage in the exhaust would limit top speed but not power off idle.
Sounds like lack of fuel, either because of a sensor or low fuel pressure. Or a vac leak.

Replace starter motor assembly with new ,not rebuilt.

burning oil ? leaks on the ground still ?

you need to remove the intake manifold to get to the right 3 plugs this is best left to a pro if you have never done anything like this before NOTE the plugs do not need to be changed till 100K