changed my house

1a. I have changed my house.
1b. I have shifted my residence.
2a. Beware of pick-pockets.
2b. Beware of pick-pocketers.
Please correct all.
Thanks.

Whilst it is grammatically correct, no one would say ‘I have shifted my residence’. It gives the impression that you picked up your house/flat/apartment and physically moved it.

I have moved (house/home)
is the natural expression for what you seem to be trying to convey…

‘pick-pockets’ is the correct term. Not ‘pick-pocketers’.

I have changed my house/residence/domicile.
I have shifted/moved to another house/residence/domicile.
(Fathima, what we should actually mean by shifting is transferring all our domestic/household articles from one residence to another. But we loosely/incorrectly say that we are shifting our residence. The verb ‘shift’ is both transitive and intransitive)

in English.

But why don’t you note, recognize and tolerate that that usage also conveys exactly the same (deep rooted) meaning in English to foreign users like us? It may be a variant, I’d say, but not absolutely unacceptable or incorrect since the very idea is well conveyed. In fact if what you suggest is used, it will be frowned upon, for it is not at all common here. Once you said: ‘I request you to do it’ should be ‘I request that you do it’ while the former is part and parcel of the English spoken/written in all walks of life. So, as you refer to certain usages as AmE often, you can also refer to such usages as InE. There is nothing wrong if you would like to say so.

As far as I am concerned the reference point for this website is standard English.

Try using your suggestions in countries where English is the mother-tongue and you would come across as extremely pompous.