Can I initiate Family Sharing from my apple ID on an iOS device as the organiser to another account on my Mac so that latter can have the possibility to share the iWork apps i have on my iOS device without buying them from the Mac Store?
Sure you can.
You can set your preferred account as Organiser, with Share my purchases switched on, then invite & add your other account as an Adult (you could set yourself up as a child, but then you'd have to ask yourself permission ;)
From System prefs > iCloud > Manage Family...
First & last are 'me'
One caveat - you need to make sure that the two addresses aren't already associated. I had great difficulty figuring out why adding my second account wouldn't work. It turned out to be [iirc] that each was using the other as the rescue or secondary email address.
As you're setting it up initially you need two devices [or accounts on a Mac] each to be signed into its own account. It took some juggling for me to set this up on a single Mac, but between iPhone & Mac ought to be simpler.
Full setup details at Apple KB: Set up Family Sharing
I'm not sure whether doing this will enable the right to the Mac version of an iOS app. It usually wouldn't, but the iWork suite & Apple's own software in general seems a bit of a special case.