Does anyone know of a site where designer can submit Photoshop/Sketch files of their website and front-end developers can convert them to HTML/CSS/JS for free or for a small fee?
Perhaps a better tack for you to learn is to find a small business or nonprofit who has a strong brand identity but has no real budget for getting their site made. (I also did this, very helpful.) On the plus side, you'll be helping out someone while you learn, and you don't have to necessarily have great design skills as its already ready already.
Lastly, just my two cents here, getting better at CSS doesn't have to necessarily be 1:1 with design all the time, but it helps to be open to working with designers and having a rudimentary knowledge of design to achieve the look and feeling that they're requesting. So maybe befriend a designer or two and pick their brain a little. You'll probably find that when working with designers in the future that they'll appreciate that you have some knowledge of what they do as well!
I would definitely recommend their services as well. I previously worked as a contractor (mostly on internal backend systems) for XHTMLized and their sister company X-Team, and have used XHTMLized (before the rebrand) for a client project of my own.
Edit: just read the last part of the OP. You will absolutely get what you pay for in this industry. If you pay nothing or almost nothing, you will get shit back.