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The code editor itself doesn't currently have spellcheck support, sorry. The "Spelling and Grammar" menu is for text fields like the Find and Replace text fields.
Textastic 5.1 now uses MultiMarkdown v4 instead of the Discount Markdown library for its integrated Markdown preview.

.mmd files automatically use the MultiMarkdown syntax highlighter, but you can also choose the syntax definition manually from the File Properties popover if you want to use it for other file extension like .md, which uses the Markdown syntax definition by default.
Textastic 5.1 now uses MultiMarkdown v4 instead of the Discount Markdown library.
How did you open the same file twice? This shouldn't be possible. Are you sure that it was indeed the same file?
Here are two screenshots of how it looks on my device:



This does work for me. Is your css file called "screen.css" and in the same directory as the html file? File names are case sensitive in iOS, so something like "Screen.css" won't work!
What does your html file look like?
You can add custom syntax definitions to Textastic by using TextMate bundles. See
A quick search for "Rust tmbundle" in Google brought up these TextMate bundle which might work:
Please try to enable the "Debug Log" setting in the connection's settings screen. Tap on the (i) button on the right side of a connection to change its settings. This creates a log file when you try to connect to the server which might help you find out what's wrong.