I am new - can I fold my own sequence de novo locally? Just for my own curiosity?
And second: can I make disulfide bonds?
Check out the "Protein Design Sandbox" puzzle that you'll find if you scroll down in the "Science Puzzles" list. The "sandbox" part means the puzzle doesn't award any points, but it gives you lots of flexibility in creating a design. You're still limited to just a single chain of amino acids, but otherwise there are few restrictions. Also, it currently has 1,577 days left, so plenty of time to try things.
Right now, the regular design puzzles (where you play for points) are focused on binder designs. There may still be "monomer" (single chain) or "symmetry" (multiple identical chains) free design puzzles from time to time. The binder puzzles and the free design puzzles impose various restrictions various types of "objectives", which add or subtract points (and slow things down), so these puzzles aren't totally "free". The "Protein Design Sandbox" has just "core existence" and "ideal loops" objectives, and I don't think they give a bonus or penalty.
As far as disulfides, design puzzles often don't allow cysteine, but again "Protein Design Sandbox" doesn't have that limitation. Many of the puzzles in the "revisiting" series can have disulfide bridges, although not this week. Turn on "show bonds (sidechain)" under "View" to see the bridges. They show up as a yellow/green spiral, similar to the blue/white spiral for hydrogen bonds. Other view options, like "show sidechains (all)" and "CPK" or "EnzDes" coloring make it easy to spot the cysteines, highlighting the sulfur atom at the tip of the sidechain in yellow.