Can a .ly domain rank on Google.com? Sure. Here are many that do:

https://www.google.com/search?q=site%3Aly

Do they have a ranking disadvantage? That's a lot tougher question. It's definitely in a gray area. Thanks to Bit.ly and some others, there is some precedent for these domains to be treated as generic, if other signals suggest they are not Libyan domains (geo-location, language, etc.), but there's always more risk for a new site and a chance you'll need to spend more to get the same results.

The political situation is much more worrisome, though, because none of us can predict that. If there's a history of .ly domains being confiscated and if that confiscation was considered legal (even in the short-term), then there's no guarantee that won't happen again. That's a risk we can't calculate in SEO terms. The fact that even Bitly eventually went to bitly.com doesn't bode well.

My gut feeling is that (1) there are no magic domain names, and you're going to have to advertise/market/promote any new domain, and (2) given the geo-political situation there is more than average risk (vs., say, a .co domain or one of the new TLDs). There's a lot I don't know about your situation, but I think your hesitation is warranted.

It is possible to get a Google Drive document indexed, but I'm not clear what this would accomplish. It would likely be a weak link (Google knows this is possible and that Drive documents are user-controlled) and it ultimately means that you're competing with your own documents for ranking. So, now you've got state pages on your site and state pages on Google Drive, both in the index, and one is potentially cannibalizing the other. I think this would ultimately be counterproductive, honestly.

I haven't seen the specific Educational Organization schema have an impact on SERPs, but they're diverging so much lately that it's hard to say. There are some specialty carousels like this:

https://www.google.com/search?q=best+colleges+in+wyoming

...that could be using it, but I suspect this is coming from the broader Knowledge Graph. Individual colleges have Knowledge Panels, but a lot of that data is coming from GMB listings, best I know.

There's no real harm, if the data is appropriate and well-structured (i.e. you're not putting a university mark-up on a sandwich shop page). The drawback is basically spending the time and energy and getting nothing in return.

I guess the other drawback is that Google could use that data to feed its own internal database but not give you anything in return. That's a drawback of basically everything in SEO right now, though.

Unfortunately, I haven't seen any studies of that nature. I typically look at it pragmatically -- is there a change in SERP features related to that schema (i.e. is there direct, measurable benefit)? So far, I haven't seen any. On the other hand, I don't see any evidence of harm, as long as the schema is appropriate and well-structured. It just comes down to where you want to put your time/effort.

You can't really "optimize" for Hummingbird, but understanding RankBrain can certainly help you do keyword research and write relevant content better.

Don't have an exact date, but the UI feature is relatively new. I agree with @effectdigital that this is a general capability that Google has been building/expanding for a while. It's helpful to look at that underlying logic, as it will spawn new features over time.

I'm not sure there's a one-sized-fits-all answer. If the .com is more geared to an audience outside of Singapore, and the .edu.sg site is more geared to the local audience you could set a region and/or language with rel="alternate" hreflang:

https://support.google.com/webmasters/answer/189077?hl=en

This is a bit more subtle canonicalization signal that Google can use to sort out sites with language and/or regional copies (the regional aspect may be relevant even if both sites are in english).

The next question would be: where does your traffic come from? If you want to consolidate, but most of your traffic is coming from outside of Singapore, then I'd probably stick with the .com - it still has a "generic" status. The .edu.sg may rank more strongly in Singapore but fall off everywhere else.

I wouldn't worry much about the DMOZ link, especially if you have a solid link profile. DMOZ links have gotten buried over the years and typically don't carry nearly the value most people think. At some point, they could be a solid boost to a new site with a small link profile, but I think even those days are well behind us.

Happy to help - hope it does the trick.

I'm checking with Dr. Matt Peters, head of our Data Science team. It's less about secrecy and more that DA/PA are based on machine learning and have gotten a bit complex. Still, I suspect we can give you a general sense of how DA/PA pass through links. Posting this because I suspect an answer may take a day or two.

Yeah, I'd have to concur - all the evidence and case studies I've seen suggest that rel=canonical almost always passes authority (link equity). There are exceptions, but honestly, there are exceptions with 301s, too.

I think the biggest difference, practically, is the impact on human visitors. 301-redirects take people to a new page, whereas canonical tags don't.

Our data in OSE can lag a bit, but I'm concerned that you're seeing the same thing in Google. Is it possible to provide an example URL?

When you say "Google is still indexing the old URLs", can you tell me exactly how you're measuring that (I find "indexing" means a lot of things to a lot of different people). It's not uncommon for both the old and new version to be stuck in the index for a while, and that's not always a bad sign. It can be, but it might not be (I realize that's not terribly helpful).

Have you double-checked some of these redirects with a header checker? It's amazing how often a redirect is supposedly in place but isn't working properly, is producing multiple hops, etc.