If I promote any others' products through their landing(squeezing) page made by them, couldn't I build a list of my own? (So, should I create my own landing page for a same product to build a list?)
If you are promoting a product and using thier squeeze page you arent building your list but theirs so i suggest you build your own squeeze page if you are trying to build a list.
Yes you are building a list for them. Why don't you do and ad swap where you send them the other person product to your list and they send your product to their list. Also look at doing solos to build a list quickly. If you are going to do solos make sure you investigate the seller because you only want targeted traffic in your niche.
I if where you I would create a list of my own, and make more money. But don't forget to build a relationship with the list.
If you still want to promote the product then you should build your own squeeze page and divert traffic there first, then divert them to the product offer page. This way you will build a list of your own