When I compare image and web, I can see that image searchers aren't counted as web searchers.
When I check positions, I can see that some search querries of one of my sites are at positions 1.1 to 1.9 based on web and 3.1 to 45.4 based on image search. Thats working - as long as it is picture search vs. web search. And as long as the search querry has no image-box.

Now your question - I checked another side wich has a lot of rankings in image boxes in web search. And I think you are right:

• Search Console is telling me I am on the web at postion 1.1
• When I Google it, my picture is the first one in a picture box at the top of the Results.
• Than there is a website (wich is not mine)
• And finally I am on Positon 2 (Picture Box, other Website, my Website)
• the same with a lot of querries. Google is here counting my image result (first result) in a picture box @ web search.

Tried to find some clients - found one. A search result he simply couldn't have with his website. But he had - it was a picture somewhere in the middle of the SERPs. I also saw that google seems to count each image as one result.

So finally you are right. If you have a Picture somewhere in an Image Box (wich is displayed in a Web Search) is a Web Search Position in Google Search Console.

Every Subdomain is a domain with own Domain Autority. In general I would not use sub-domains - in a few special cases it is a good decision, but normally a sub-domain is a new domain starting at zero. I like Landing Pages and Blogs in subfolders wich helps a lot for the existing domains autority.
By the way, links from subdomains du other subdomain (www, etc) are treaded like internal links.

Q:whether having subdomain like this would affect the traffic metric and ineffect affect the SEO and Rankings of our site
A: It would be better if it's a subfolder, but yes it will affect in traffic and that allways could lead you to better rankings

Q: does not affect the increase in domain authority
A: correct

Q:considered as seperate websites
A: yep!

Q: wanted to make sure that it does help in the overall domain
A: Like I said in A one it would be better with a subfolder (special the blog) but it wont hurt you

Sounds like you have an mobile optimized Website (responsive, correct redirects, somthing like that) or your website has a pretty good User-Experience when it is used on mobile and some of your competitors don't.

For more Tipps we need more details

@ayofztk it doesn't work. Just google tech crunch and only tech crunch domain has tech crunch in domain name. A little special here, that's a navigational query.

You can rank with an EMD when the content is good enough, the popularity is good enough. Just a Keyword in a domain name doesn't help. Going away from a .com domain to something like you did ".blog" is also not the best idea,

Don't know really what you mean... Did you mean the SERP overlay? In that case: total/all external links.

For Linkearning you need content wich is readable/shareable/linkable - really great stuff with a lot of value for others, without great content it is a Mission Impossible. So if thats part of your "onpage" - you need great value to share with the right people.

It's hard to answer this question, we don't really know how far u are and what you exactly mean with onpage or what the site's content is.
I think Links to products are pretty hard to get. You need content round about your products, linking to them. Outreach for Links to products could make you sad and depressive ...

PS: I think Rands last WBF helps a lot in saving time by do outreach in a better way: https://moz.com/blog/link-building-outreach-in-a-skeptical-world-whiteboard-friday

I think you could have is the following problem:

You got a Domain wich earned Links bevore and these Links are still out there. Google can see them and you will again and again see them in WMT. 
You cant just say solved and than they are gone, caused by the backlinks. They come again. 
Check that in WMT - I dont know how it is called in english versions (I just see the german), you can click on the 404 and than take a look at "what is linking to that page"
An easy solution in that case may be to disallow "/fs" for bots. (if you dont use fs in your url structure)

Sidewide Footer Links (ideal with Keywordrich Anchor) are awful. Nofollow Links shouldn't be a Problem, so you can ad that in your themes. You could kill them by yourselfe or change the default value for linking to theme author.

There couldn't be any good thing on such a link, so nofollow I think its ok, no link is better
Thats 2010-SEO and burried long time ago.

For the Links you allready have: You know your Linking-phrase, so:

search the web for that phrase,
sort them by domain,
make a disavow-file with these,
Submit them (thats what I would do)

By the way: Some Theme-Users are not to clever in SEO/Webdesign/Programming - they may simply change your link-class to "display:none" or change the link-color to background color. (I have seen a lot crazy things, including Theme by: zensored cheapest flights

If you have redirected the URLs correctly you should fatch the homepage as Google in WMT and send them including all refereing links. the new URLs are pretty fast in SERPs than.

The rest is like Ryan Purkey said - thumb up

This is a thing wich is pretty much normal for a lot of CMS-Templates. It is not best practice, each SEO-Tool will tell you to use only one h1 wich is unique. Don't have equal H1-Tags everywhere. Thats the best practice.

According to John Mueller and my experience, Google is not stupid. It is possible to have more than one H1-Tag. Now it depends on how much factors you are serving well. You and your competitors. These H1 alone is not such a big factor. It is working if you have a second headline with the main-topic of your website. A lot more stuff is relevant. If it is not easy possible to change it, you can deal with it and care about other factors.  Special if they are in different sections.

If it is possible, I would allways follow best-practices (specially for smaller or newer domains/companies). One thing sounds wrong "he H1 text being the brand's name, as this is what we'd want the title of the page to be" - I mean, the title (bet you ment the h1) should be what the page is about.  Without alt-attribute you current H1 is a simple image, wich means it is empty.

You ask what is working better - Better is to have an H1 unique on every page. Dont use Headings as style Elements and yes, give an alt-attribute for your logo. Thats defenetly a better way, but it is not impossible to do like you did. Like I said, I am pretty long in this business, thatswhy Logos, Sidebar- & Footerheadlines, all style Elements are not SEO-Elelements when I create Webpages. But yes - I also work for websites without changing h1-logos and h3 menu-items (cms-reasons). And it is possible to rank in hard topics. Favorite answer - it depends.