Will apple stores repair or service the iPhones that have been just OPENED before from a non-authorized shop?

will apple take in my phone for any future repairs or replacements after this?

None of us on a user-to-user site can tell you in advance what Apple will do.

You can try, but Apple will probably refuse to even look at the phone if you tell them that another shop has been inside the phone. So, you might not want to offer a lot of information.

Whether you choose to tell or not, if Apple detects that the phone has been tampered with, or if they detect any water damage, they will refuse to service the phone and go over your options with you.

It will be up to the specific store you choose as there is not a single policy that I am aware of that would prevent it, but it has been reported here that most won't as they will no longer feel comfortable with having a warranty on the work they perform when the device was previously tampered with.

In addition with liquid damage, there are liquid detectors inside the phone that will indicate that the phone has had liquid spilled and it has went inside the device. This is further reason that the phone may not be serviceable and replacement may be your only option.

It will probably be at the Apple Store or Apple Authorized Service Provider's discretion for service support. As soon as a non-authorized service provider tampers with your iPhone, your iPhone will probably be rendered ineligible for service support from Apple.