Do I need my phone with me to use the card when abroad?

Do you need to have the phone with me when I use the Revolut card when abroad and if so, do you need to have Mobile Data turned on (which can be expensive when roaming?

I see something about a ‘Two Step Verification’ process on their website but when I’m on holidays I like to leave the phone in the hotel. Will I need to enter a code into the phone everytime I go to use the card and if so, is the code sent by text or over the internet?

(I will be doing any topping up from the hotel in the evenings)

you seem to be mixing many things in this matter.
no , you dont need your phone to use your card, but make sure you disable Location Security or it might block some payments.
You do need your phone to top up the card, if you use all your money.