You can open an .xlsx file without Excel in a browser-based editor, in LibreOffice, in Google Sheets, or in a text editor if you only need the raw XML. The differences that matter are whether the file gets uploaded, whether formulas survive, and whether you can save back to .xlsx rather than exporting a copy.
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Yes. LibreOffice, Google Sheets and browser-based editors all read .xlsx without an Excel licence. The trade-offs are install size, whether an account is required, and whether the file is uploaded.
It depends entirely on whether that tool processes the file locally or uploads it. Check for an explicit statement; if a tool does not say, assume the file is being sent to a server.
Only if the tool is a viewer rather than an editor. A viewer keeps the computed values and drops the formulas, so saving from it flattens the sheet permanently.