Is such participle clause reducing usage constrained to only past tense?

Question

As I saw on a grammar website, "She went into the home and left her shoes" equals "She went into the home, leaving her shoes". Can this usage also be used with other tenses? Like future tense, present perfect tense, etc..

P.S. I mean, does the sentence "she has been working AND WRITING composion in her office" equal "she has been working, WRITING composition in her office". .... and does "I will pay for it AND GIVE SOME PAMPHLET to you" equal "I will pay for it, GIVING SOME PAMPHLET to you"...etc.

Here is the source that describes an action that happens just before another action.

Answer 1

The section of the source to which you pointed (an action that happens just before another action), has the participle clause and the main clause reversed. If you apply the same reasoning to your sentence, it ought to have been

Leaving her shoes, she went into the home. equals
She left her shoes and went into the home.

In your first sentence the act of leaving her shoes is placed after the act of going into the home (connected with 'and'):

She went into the home and left her shoes.

which suggests, according to the website, that it could be written as

Going into the home, she left her shoes.

So, to answer your original question, no, those are not equivalent as far as the explanation "action happens just before another action" is concerned.

Answer 2

As you may know, English does not have perfect tenses: only infinitive, past, present, and future. But we can approximate the perfect tenses with some (slightly awkward) grammar constructions.

She will have gone into the home, leaving her shoes.

She had gone into the home and had left her shoes.

(Sorry, I am stumped creating a present perfect sentence.)