Sentences

Yes and yes.

Mister MicawberYes and yes.

Thank you. By the way, which part of speech does the word 'pampered' belong to? Is it a past participle verb or an (-ed) adjective? Moreover, can we use either of the two after 'being'?

These are argued about so much that I refuse to consider the difference any more.

His work tired him, so he is tired.

I will let others discuss this.

Alright. Anyway, Is there any rule or trick that can tell us when we can replace, in a sentence, a present participle with an infinitive or vice versa?
e.g #1: I planned to go to some real Italian restaurants.
Would it be correct to say it like this without changing the meaning:
I planned going to some real Italian restaurants?
e.g #2: It didn't stop raining all day yesterday.

LeGion12359 Is there any rule or trick that can tell us when we can replace, in a sentence, a present participle with an infinitive or vice versa?

No; each verb has its own relationship with those complement forms.

Some take only one: I planned to go.
Some take only the other: It stopped raining.
Some take neither: (X)

Mister MicawberAnd you need to learn each relationship individually

Oh! It would be really difficult to learn and remember each relationship individually. There are so many different verbs in the English language. How can I do it? There must be some trick/hint for non-native speakers.

LeGion12359here must be some trick/hint for non-native speakers

Nope.

LeGion12359What's the difference between the two?

I forgot to lock the door. = The door is still not locked; I forgot to do that.
I forgot locking the door. = The door is locked, but I forgot that I had locked it.

Mister MicawberNope.

Well, I have to find some other ways to cope with it then.

LeGion12359Is there any ambiguity in the second one?

No; the meaning is as I have given it. It means that I locked it and then forgot that I had done so.