How are Japanese company division, section or department names usually translated to English e.g. 「システム開発1部ソリューション１課」? Does it translate it to System Development Department 1 Solution Section 1?
It really depends on the company but I work for a department similar to one you described (minus the numbers) and it is translated quite similarly to what you have said.
Some discrepancies would be things like whether the department is written as a Kanji-base or a Katakana-base.
Also note that some companies do not use 課 but instead implement team names or project names / acronyms instead.