The noindex,follow tag on paginated pages will not compromise your sites integrity with Google. I think it's important to look at your site as a whole and divide the number of all pages by paginated pages.  If the ratio is above 10%, I would be concerned that the site may appear to be more of a directory and it definitely would make sense to noindex the site. Also, there are paginated pages with just a bunch of links and other paginated pages with a lot more data surrounding the links. The fact that others are ranking higher probably have more to do with overall site content and PR.

Is this for a national site? if so, you will need to further segment the URL  placethatsellsusedcars.com/used-fords/de/dover or if you have multiple pages for the same city, you can furthe segment the URLS by zip code - placethatsellsusedcars.com/used-fords/de/dover-11010. Most importantly is that you provide user value on every page and the pages don't seem like duplicates to each other. Google frowns on directory sites and you need to provide much more value then just a directory of links.

subfolders are better than subdomains, it's all under one site instead of 59 (according to obama) individual subdomains.

that was an old school strategy when Google really gave push to having the keywords in the domain name and spammers took advantage of it to rank better by creating subdomains for each keyword phrase

if the linking is exactly the same it should have no effect on SEO, but could have a neg or positive effect on bounce rate and other user experience stats.

you could always safely a/b test it

I'll give you a direct answer. No. Directory submission sites are no longer relevant due to search engines, and they are seen by Google as nothing more than sites designed to sell links and pass PR.

Smart link builders stopped this activity years ago. There are only a small handful of directory sites like yahoo that are worth submitting. 99% of them are not.

If you find a directory site that is in your niche and nofollows your link then it might make sense to get listed as a possible traffic driver.

It takes a lot to get your site removed from Google index, the easiest way is to be hacked then your site gets banned until you remove those links.

What would most likely happen with directory submissions is that the keywords you are targeting get suppressed in the rankings, you go from page one to page 50 for example and your traffic drops. Google emilas you a letter in WMT saying they detected unnatural link building and then you spend all sorts of time trying to get your links removed and disavowing and resubmitting for reconsideration.

Directory sites are dead, if you're going to do link building it needs to be one offs to individual sites who have never sold links, not on sites who's sole business is to sell links.