Try this in your .htaccess file:

RewriteCond %{HTTPS} off

First rewrite to HTTPS:

Don't put www. here. If it is already there it will be included, if not

the subsequent rule will catch it.

RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]

Now, rewrite any request to the wrong domain to use www.

RewriteCond %{HTTP_HOST} !^www.
RewriteRule .* https://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]

I always include the brand name where I can, but if it is too long because of that I do not hesitate to drop the brand name.

For the titles, whilst I think about it from an SEO perspective, it is also important to think of it from a CTR perspective too.  Sometimes you need that extra bit of description at the expense of the brand name.  To give an example, on some articles I find it better to put the month and year at the end instead of the brand name to increase CTR.  So basically, no I don't think it particularly matters, but it will vary on a case by case basis.

Actually, many of the larger hosts using cPanel now do not require a dedicated IP as they use SNI technology that allows an SSL certificate to be installed on a shared IP.  However, there can be other benefits to having a dedicated IP such as being less likely to get caught on an Email blacklist etc.

Is there any reason to use relative Urls from an SEO perspective?

Thanks, that was my impression of it as well.  Just wanted to check I wasn't overlooking something.

Aman,... well what you are doing is creating thin pages which over time might just risk a Panda Penalty.  You might want to at least no-index those blog pages.

Not necessarily.  He could be using Nginx as reverse proxy.

He already said the http to https is working fine with my suggestion.  The problem is the redirect from one URL to another which what I gave him for the .htaccess doesn't address at all.

ie.

https://www.directtraveller.com/holidays/about-direct-traveller/british-travel-awards.asp
to
https://www.directtraveller.com/awards

You need to be really careful doing this.  Whilst that used to be pretty much the industry standard, Google recently updated its guidelines to do with Doorway pages.  I am not sure that these new algorithm changes have been implemented but it is exactly this method that it will affect.

So, until we know what is up with that you will need to proceed with a bit of caution, and at least ensure that all content on those location pages are completely unique.

http://googlewebmastercentral.blogspot.co.uk/2015/03/an-update-on-doorway-pages.html

Are you able to share a link to the page in question?