1. Not sure about the range of Shandong.
2. Using diesel as primary propulsion is out of the question. The 003 will likely use gas turbines + auxiliary diesel units, or steam boilers + turbines. So far it seems that steam is more likely. The advantage of steam propulsion is an easier transition to nuclear, as a nuclear reactor is basically just an infinite steam generator, which is then coupled with steam turbine for propulsion. China has some experience with steam propulsion on the 001 and 002 already.
3. You typically find diesels in every modern warship but only for auxiliary power. Using diesels for propulsion was a thing at one point, but it's not very common these days because diesels struggle to get up to speed. Diesel is more widely used on commercial ships as they perform well at low RPMs (better for cruising) whereas gas turbines are only efficient at high RPMs (better for speed). And even now, there is a major shift away from diesel and towards LNG and gas turbines for commercial ships, due to emissions regulations.
So, modern warships typically have a 2-4 small diesels (~5 MW per unit) for long-distance cruising and small power generation, and 2-4 gas turbines (~20-40 MW per unit) for when you need combat speed and big power generation for radars and weapons systems. In this regard, you will likely see diesels on the 003, but propulsion will not be their primary role. They might only contribute to 30-40 MW of power generation out of the 150-200 MW that a 85,000-ton CV will require.
If I remember, the Type 903, Type 901, Type 071 and Type 075 are all powered by diesel. Greater use of diesel is not surprising for Chinese shipbuilding industry due to the rarity and expense of building gas turbines, where the manufacturing remains limited and prioritized to somewhere else. Why the Type 054A frigate and 056A corvettes are diesel powered when similar class ships in other nations are using gas turbine.
This does not change that 003 will either be gas or steam turbine with diesel as auxilliary.
I don't agree with you however on the fate of diesel engines in commercial shipping.
The large majority of Chinese commercial shipbuilding, talking about the mega sized box ships, bulkers and tankers, are powered by piston engines, four stroke, and the bigger ones, two stroke. China is already designing and making these engines, but they are also making engines under license from MAN and Wartsila from Germany.
LNG powered engines are dual fuel engines, either diesel, gas or steam turbine. They can burn fuel oil or LNG. Diesel is not going anywhere, It has about 50% of the commercial ship market, and is dominant among box ships, bulkers and tankers, while turbines are more likely what you see in cruise ships, ferries and ROROs.
Biggest LNG powered ships in the world are the container ships of the Jacques Saade class. These monsters are about 400 meters long and 61 meters wide, with a capacity of 23,000 TEU. The engines are referred to as 12X92DF is said to be the biggest Otto cycle ever made. These engines are a partnership between CSSC and WinGD (Winterthul Gas and Diesel) using the Wartsila two stroke.
Look at the size of the crankshaft. Lol, the piston rods are monster sized. Yes, its built in China.
The engines go into these ships.
The LNG tank used on these ships are as big as a submarine, and from the air, the tank can be confused as one.
By now it should be familiar where these ships are being built. That's in Jiangnan. We see these ships often in those flybys over the Jiangnan shipyard right next to where 003 will be built, along with a fleet of destroyers.
Five of these ships are contracted to Jiangnan, and four to Hudong Zhonghua, to be made in HDZ's new yard in Changxing Island near Jiangnan's own facilities.
Despite that 003 is being built right next to the world's largest LNG powered containerships with the world's largest piston engine ever made, it won't change that carrier is going to be mainly turbine powered with diesel auxiliary.