If websites have good DA will be trusted as per Google norms.

I do not believe that this is true.  I think that DA and "trusted by Google" are very different things.  I think that some sites with very high DA are not trusted by google and penalized by google.

I think that links to or from some high DA websites could be harmful to your rankings.

I would like to hear Moz or Google respond to this.

This is called.... "Surviving between the bomb craters."

It is actually a pretty common thing.   It is like people who drive over the speed limit all of the time but they just have not been caught yet.  They are simply "damn lucky".

So, I would not put much stock in improbable events.

Once I get to the point that I would not do something on my own sites.  I am unable to give further advice.

Try it and see what happens if you think this is a good thing to do.   I don't.

I have no opinion on this.  It might work, it might not.  I would not do this on any of my sites.

I think you are starting with a small amount of seed content and spreading it very thin through many pages.  I can't imagine how this would produce a good experience for users.

I have added large numbers of pages to websites and the result of that has often been a decrease in rankings even if the content was golden.  Why?  As Dr. Pete says... the authority and link value of your site gets spread out into a larger number of pages.

If you add an enormous number of pages and have a puny amount of links delivering spider activity to your site, google will start to forget your deep pages if they are spidered infrequently.   If you add 10,000 new pages then you better have a few dozen permanent links of about PR4 or PR5 hitting nodes located deep within that mass of 10,000 pages.  That will force a constant stream of spiders deep into those pages and they will have to chew their way out to escape, indexing pages as they go.  Remove those links and the stream of spiders stops and google might forget those pages if they are on a site of less than moderate strength.

The only way that you get your rankings back after adding a huge mass of pages is if your content is engaged, shared, and linked enough to earn it back.   Every page on your site adds a bit of weight, it has to be supported with authority.

Huge powerful sites, even those with lots of very high quality, highly engaged content, can be hit by Panda.  I had a bunch of republished and thin pages on one of my sites and it lost rankings in a Panda update.  I deleted lots of those pages and noindexed others and rankings came back.

If the number of pages on this website increases to 10,000 can that decrease its domain authority or affect it in any way?

Are you adding gold or crap?    Gold?    Crap?

I bet content on that topic would be good linkbait.

Forums take a LOT of work.  If they want the forum to be successful and reflect well on the company then they should put it on the main domain where their name is on the line and all of their clients will see it and have an opportunity to check it out and use it regularly.

If they are not serious about this then just put the forum in an outhouse where nobody will see it.  It's going to die because they are not dedicated to it.

There are more of these than you have time to chase.

Improve your own site and forget about this is the best use of your time.

These are usually businesses who have robots that crawl the web, grab sentences, grab images, grab URLs and slap them together onto a website.

They often have crappy programmers that screw up the format of the site or make other errors.  One error is miswritten URLs that hit error pages on your site.

This is a common problem.  All of my sites have these types of links.

Cussing provides some relief.

Weasel businesses with incompetent programmers.

Not much you can do about it, unless you want to go to China and grab them by the tie.

Only robots who don't buy anything.

Yes, that is better.... but you will only be able to do it on websites that tolerate unpaid advertising.