A) A few days ago it started getting redirected to sites like 'adult app' and '18 and abused'; both sites I have NEVER visited.
The first site that redirected me to it was Failbook.failblog.org, then the newspaper site The Mirror. Neither are 'dodgy' and certainly aren't porn.
I'm confused as the above is a contradiction? I don't think "The Mirror" would redirect you to an adult site for extra revenue no matter how badly paper sales have gotten.
Anyway as I had recently downloaded an app that I was a little unsure about the safety of...
If it was originally installed from Google Market then you should have little to worry about but be aware somethimes things sneak through. It's happened before but it's not often.
What IS permitted is for applications to contain triggers like AD popups, nag screens, and opening sites. You should review and read all the rights and requirements you agree to before installing any app.
I would suggest you look for an "Ad Blocker" and install it to help minimise this sort of thing. You can use this link to start reviewing but I don't recommend any paticular one.
You can also look for an anti-virus app as well, some come bundled, but stick to the vendor names you know like Nortons, Avast, Kaspersky as an example.
I haven't had the same issues on computers and hadn't visited anywhere dodgy.
I didn't say you had, I noted that using your smart phone was no different than using your computer.
The only thing that doesn't make sense is the "Adult App" and "18 and abused" redirects you note. I wouldn't think that would be allowed for any legitimate app on the market. Clean out any browser links or bookmarks you have that aren't added by you and keep an eye on things. Are you still being redirected to the sites you noted earlier?