I am invited as a speaker to a international conference to present a published paper. I want to ask if is it usual to not pay the conference fee and the hotel? Should I ask them via email?
The larger and more prestigious the venue, the higher the probability that your conference fee and travel costs will be paid by the venue. Certain invited speakers (particularly keynote speakers) will also be given a speaking fee, but "invited speaker" means different things in different venues.
You should, therefore, explicitly ask. First, if it's a small and not well-funded venue, they may be asking for you to volunteer rather than offering to pay. Second, many predatory / scam conferences send out official "invited speaker" invitations that attempt to stroke your ego and get you to give them money.
If you don't already know the people and the venue, be careful because it is quite likely to be a predatory / scam invitation. The "invited to present a published paper" is a particular red flag, as these venues seem to have a semi-automated method of scraping publication databases and inviting authors to give them money to talk to a half-empty room of others who have been similarly scammed. Once you've published a few papers, you'll get a lot of these---I get several per day.
"Invited speaker" is sometimes overused, misused or misunderstood. While key note speakers (also called plenary speakers) usually get funding (no fee, travel and housing support...) the same is not true for people who are invited to take part in a minisymposium at a conference.
Also there are conferences who send some "invitation letter" to anybody who submitted a contribution and got accepted (this true for some real but also for fake conferences). And then there are fake/bogus conferences who send spam emails and invite anybody as a speaker.