Generally I find that low quality links take a long time to display, I find that higher quality links tend to show up very faster - for example if you was to get a back link at the bottom of Stack Exchange or Facebook for example I'd bet you'd have your link listed within a week.
Low Quality Links
Low quality links are generally on low quality sites that are not crawled very often, and of course if the site is not being crawled then they will not find your link, additionally web directories are little value in terms of SEO and Google does not crawl these often as you may think, I've run several directories sites and if they are receiving hundreds or thousands of pages added daily then they will take months to enter the index, never mind find your link.
Tread Carefully With Self-Creating Backlinks
Your biggest concern should be is that your creating your own links which Google considers manipulation which they do not welcome with open arms, you have mentioned anchored keywords on your links, you really need to tread carefully when making keyword anchors these days, if you use them on low quality sites or if you just have far to many anchors the same then Google will just start to de-rank you for those keywords, or worse your whole site will receive almighty slap with the likes of Penguin V2.
I personally believe that the most powerful links are those with no anchors because simply because I see it as more natural, most people who link on the internet do not even know what an anchor link is, and on forums so many people forget to use the BBCODE and if you look on this site many people do not link using keywords they use sentences that sometimes contain keywords...
Make Links With Communities
The best type of links these days are generally ones on Quality sites, a cleaner link profile will help you in the long run, Guest Blogging and joining communities within your niche remains the best way of creating links if the administrators of those sites allow it. (Not talking article directories, these are evil...).
There is no difference in terms of indexing of your backlinks if the link is nofollow or without, Google and Moz, Majestic use nofollow in their metrics which basically gives you a citian flow, trust score and moz score and so on... It's very unnatural to aim for all dofollow links, in fact these days its better to have more nofollows than dofollows because its extremely unnatural... Google knows that the majority of links these days are nofollow and if you have 90% follow links then that rings alarm bells and your site will be flagged.
I recommend you take a look on the net and try to read as much as possible before engaging in making your own links, if you believe you have read enough and a lot of this answer does not apply then ignore and hopefully others will find this page useful.