"Can I use my current US Steam account with my US game library (2,500+ games) in Mexico?"
Yes. Past purchases are unaffected when you change the country of residency.

"Can I purchase new games from the US Steam store, while living in Mexico?"
That depends on if you are simply visiting or permanently moving to Mexico. If you are no longer living in the US then you need to change your country of residence to Mexico. To do this you will need to first move to Mexico, then make a purchase with a payment method that has a billing address on record in Mexico. Note: You can only change your Steam account region once every 90 days.

"I don’t want to set up a new Mexican Steam account, because I don’t want to purchase all my game library again."
You will not need to repurchase games or create a new account. You need only to change the account Region which you do as per above.

"Moreover, I don’t want to purchase games in the Mexican Steam store even if they could be cheaper because I think that is something that Steam rules or/and terms of service don’t allow."
Actually, residing in one country while keeping the Steam account region set to another is against the SSA. If you are residing in Mexico, and no longer live in the US, you cannot keep your Steam Account region set to the US. Furthermore, if you later return from Mexico to live in the US, you will need to change the region back to the US. Note the 90 day restriction.

"Anyway, I don’t have any Mexican payment methods."
This is going to be a problem since you cannot change your Steam region without a valid payment method. Even if you no longer live in the US, you will need to change the address for your US payment methods (checking, credit cards, etc.) to your place of residency. Here you may have problems since not all US financial institutions allow for an address in a foreign country. You will need to contact them for advise. Practically speaking, you will only need one payment method that is accepted by Steam with a Mexican billing address on record to change the region setting of your Steam account.

"Basically, what I want to do is to continue using my US Steam account, purchasing games in the US Steam store with my US methods of payment, while living in Mexico. Can it be done?"
You can continue using your Steam account, but you cannot keep the region set to the US while you are permanently residing in Mexco. Whether or not Steam games are more expensive in the US than in Mexico does not matter according to the SSA. Any difference in pricing is problematic. Trying to work around this restriction is grounds for Valve to terminate your account. See Section 3A of the SSA:

You agree that you will not use IP proxying or other methods to disguise the place of your residence, whether to circumvent geographical restrictions on game content, to order or purchase at pricing not applicable to your geography, or for any other purpose. If you do this, Valve may terminate your access to your Account.

Originally posted by lfgm2010:

I am planning to move to Mexico (2025), I’ve had a US Steam account for more than 15 years. I need help with a few questions, because I have never used my US account in Mexico. I am planning to keep my Steam method of payment, my US Paypal account linked to my US checking account.
Can I use my current US Steam account with my US game library (2,500+ games) in Mexico?
Can I purchase new games from the US Steam store, while living in Mexico?
I don’t want to set up a new Mexican Steam account, because I don’t want to purchase all my game library again. Moreover, I don’t want to purchase games in the Mexican Steam store even if they could be cheaper because I think that is something that Steam rules or/and terms of service don’t allow. Anyway, I don’t have any Mexican payment methods.
I am just fine waiting for the multiple Steam sales discounts in the US store, like I have being doing for many years here in the US. Basically, what I want to do is to continue using my US Steam account, purchasing games in the US Steam store with my US methods of payment, while living in Mexico. Can it be done? Any reliable advice would be greatly appreciated!

Just to add to what's already been said...

There's a good chance that Steam will see you in Mexico for an extended amount of time at some point and switch you over on its own. When? No one really knows but it has happened.

Having a Mexican based Store won't mean you have to buy your entire library again. What you already own will be playable in Mexico. The only exception to that would be if there was a game the Mexican authorities have outright banned, but as far as I know there aren't any titles sold in the US that you can't play in Mexico.

You should be able to continue buying with a US based method at first. Everyone is capable of traveling across international borders, so Steam has some common sense to not require a Store currency change every time someone goes on a holiday. But if I were you, I would at least look into and secure some form of Mexican based payment method that you can fund just in case, even if it's only to top it off with $100 worth of pesos to facilitate a future game purchase. Might be wise to have on hand anyway in case of emergency. I've not visited Mexico but I have to assume there are some places where American Express just doesn't reach to down there.

Thank you very much for your replies and informative and useful info, xarvn and rawWwRrr. I guess I will have to change my region to Mexico and get a Mexican payment method then. I am planning to reside in Mexico 10 to 11 months of each year.
I don't think I would have a problem with the US payment method while in Mexico because I will remain having my U.S. address using a family address home here in the US. But with the change of region, I will have to open a bank account or something in Mexico. I don't know if using the Steam Wallet, adding funds, would be enough for a while to purchase games or if there's going to be an exchange rate fee for buying games in mexican pesos using US dollars, but I think that would be the case, plus whatever extra fees my US bank wants to charge too.
For example, usually purchasing games form Fanatical or CDkeys, my US bank charges $2 USD each transaction, regardless of the amount, I think both companies are based in the UK. When I purchase in Steam or Humble Bundle, there is no charge because they are based in the US. I will find out soon what's the case in Mexico, I just don't want to have problems with Steam. Thank you again!