In Oct, plan to spend 10 days in Slovenia, then head onto Veneto before flying out from VRN. Will have 11 full days in Veneto, with Padua and Verona as bases. Besides these 2 cities, would like to do day trips to:
Vicenza, Ferrara, San Marino, Mantua+Sabbioneta, Brescia, Sirmione, Aquileia+Cividale del Friuli. (Have already been to Venice, Ravenna)

Originally, was thinking pick up rental car from Trieste and return in VRN but that comes with hefty one-way drop-off penalty. Another thought is to go from LJU to VRN somehow and pickup a round-trip car rental from VRN. Have driven in Italy and aware of ZTL and limited parking.

Would also consider a mix mode of using train/bus if feasible and rent car for a day or two otherwise. Given the day trip destinations listed above, which ones are easier with train/bus versus car from Verona/Padua?

Lastly, for Aquileia+Cividale del Friuli, since will be coming from Slovenia, what is the best way to do that with/without a car? Overnight somewhere?

I think a mix is great
advice on seat61.com
rome2rio is a great planning tool, some data set errors, but for rough planning good. The first bit of data you get to see is for RIGHT NOW. So if you are searching at 10 at night (Italy time) you will see a lot of night bus info. That is alterable but take care.

Thanks for the helpful info. Sounds like train/bus is the way to go.

1. For train, is there a good app to check schedule and buy tickets before getting to the station?
2. For bus, does each city has their own app that shows schedule and track location of the buses?

TrenItalia is the official national train company. They have both a website and an app. But google maps if you switch to train mode should show you all the options both train and bus. I can't promise Google is perfect but it's good enough for initially planning then head to the train company website and make sure

https://www.trenitalia.com/en.html

You'll need to use Italian city names.

They have an app. If you create an account your tickets will show up on the app.

Almost all the places you mention are accessible by train (check trenitalia for journey times and frequency). Aquileia may need a combination of train and bus, depending on where you're coming from.

To get to Cividale, take a train or bus to Trieste or Gorizia, then train to Udine and another train to Cividale. Note that recently there have been bus replacements on the train to Cividale but I don't know how long that will last. There are also infrequent buses from Gorizia to Cividale, which is straightforward. Cividale is an attractive place to stay overnight (or longer).