Did you say when you are travelling? If so, I missed it.

Anyway, I live in Amsterdam and the weather here in the autumn will be not cold, but there will be rain showers. Dublin will probably be the same. Paris and Rome will be warmer.

In answer to your packing question, I would recommend to pack light. Europe is not a "territory" but a collection of advanced countries not unlike your own. Anything that you forget to bring, you can probably buy here (clothing, toiletries, etc.). I would recommend bringing several long sleeve and short sleeve shirts, a fairly light waterproof jack (with hood, if possible) and a sweater or two of different thickness. If you can post the specific dates, I may need to modify this.

Getting from Amsterdam airport (Schiphol) into the city is done by train. Usually there is plenty of room. In Paris, you will need to either take a bus or use a combination of commuter train and metro. Rome, as I recall, is also train. I don't know in Dublin.

I would spend at least one, possibly two days walking around the cities you will visit. This will give you a feel for them. You could then spend one day visiting the standard tourist sites. If you plan on never coming back to Europe again, you might reverse that plan.

Public transport in Europe is generally between very good and excellent. From my experiences in the US, it will be quite different from what you are used to. If you have any questions about that, perhaps I can help you.