we would have to see the site in order to give an accurate reply, but off the top of my head I can think of 2 ways of doing it:
1) use an expired or non-dropped domain (that has good authority), as these domains tend to re-rank based on the authority alone for easy keywords, and then just point a few web 2.0 backlinks to pages that almost rank (ie. rank in top 20 based on the domain's authority alone, but not in top 10 yet)
2) or, if the domain is new, they most likely target very low competition keywords, with good content and on-site SEO (well siloed site, good navigation and internal linking, schemas, etc) and - just like in the other case - the web 2.0s are enough to give the boost needed to break into top 10.
It's also possible that their site is fresh and are ranking like many fresh site do initially, and the web 2.0s are misleading and making you believe they are actually the reason for which the sites rank when in reality it's just google giving the site free rankings like they do with many new sites.... It's also possible that the sites are using strong (but hidden) links that you can't see, and it's those links that do the magic while you can only see the web 2.0s and think that they are the ones that help ranking....
Anyway, like I said, we would need to know the site + keywords + ranked pages in order to be able to figure out what the deal is, until then we can only make assumptions...
there's no number written in stone, every ranking is different. You just build links until you rank, no matter if it's 1 link, 100 links or 1 million links, you build them until you reach top 3 or #1 or whatever your goal is...
And I'm speaking about good links here, not about web 2.0s which most of the time don't do squat, so keep this in mind too!
depends on which pages you point the links to.
For homepages, mostly branded anchors (if you do have a brand, otherwise a mix of everything), naked URLs and exact / partial match anchors
For category pages I would say a mix of generic and exact / partial match anchors
For content pages (well, for blog posts at least as for product pages on ecom sites things might be different) a mix of all types of anchors (except for branded anchors, I personally don't see the point in using branded anchors on blog posts and other info pages)
Anyway, check this out, it might answer some of these questions:
https://www.blackhatworld.com/seo/guide-how-many-links-per-day-week-or-month-should-i-build.1502403/
it depends on how tough the keywords are. If you can break into top 10 (or at least top 20) with just a few links it's usually not needed to use tiered linking (ie. build backlinks to your main backlinks), you just need to point even more links directly to the page until it ranks where you want it to (or you might need to boost the overall authority of your site as sometimes high authority boosts the rankings of lesser pages on its own)...
If you can't break into at least top 20-30 even though you have more and better links than your competition you almost guaranteed need to do tiered link building, but your tier 2 links need to be pretty good / safe too (cheap PBNs, guest posts, web 2.0s, edu/gov links, etc)
These being said, even if you don't need tiered link building, you will probably still end up using it anyway (for example if you use paid indexing services as these services sometimes blast your links with low quality links which turns this into tiered link building whether you want it or not