Is it doable to convince a company to take you under their wing as more of in a apprentice role and teach you more?

Treehouse just updated their career resources pages. With tons of information to get you on you way. http://teamtreehouse.com/career-resources

There's a lot of "stuff" here to learn. Learning the skills are only part of the equation. You have to translate to companies that you are able to do the jobs they want done. It also depends on your stage in life. Internships and apprenticeships manytimes have an age restriction on them. Like my 17 year old daughter can get a paid apprenticeship in graphic design (with no prior experience).. But I would be looking for an entry-level job or freelance work instead.

Yes. Absolutely. You know what you know, but development is a position that is always learning more. You can always get better, learn more languages, expand your areas of expertise. As Cherie mentioned, check out the resources (they are really good!) Build a portfolio, show your skills, do some contract work, and get a permanent position somewhere you want and keep learning while on the job. It's why junior positions exist.

It depends on the company of course, in most cases no. You'd have to apply for an existing position and most of them require 2 years of experience. The most obvious avenue is to build a portfolio of work and then try to convince someone to take you in a jr position.