1. Although having a knowledge of Spanish,he attended the course.

本句在 Although 之后不是省略了 he was，而是在表示让步意义的现在分词短语之前，特意加上 Although，以明确该现在分词短语表示“让步状语”。又如：

Although having achieved considerable success as an artist, the young man keeps working hard. 

尽管这个年轻人作为一名艺术家取得了相当大的成功，但他仍然努力工作。

Although having questioned the suspect for two days, the officer didn't attain valuable information. 

审问了嫌疑犯两天，但警官还是没有得到有价值的信息。

2. No matter filling the technology gaps or making the breakthroughs in core technologies, Huawei is committed to making people’s life better with technical innovations and serving the national economic and social development.（误）

No matter 引导让步从句，需要接 wh-word 引出从句，即：No matter what/when/how...+ 从句，而不是 No matter doing... 故为错误。

3. Whether filling the technology gaps or making the breakthroughs in core technologies, Huawei is committed to making people’s life better with technical innovations and serving the national economic and social development.

whether...or... 可以连接两个对等成分，表示让步，不一定是完整的句子。我认为，应该在 filling 和 making 之前加介词 in，表示“在......方面；在......过程中”，改为：

Whether in filling the technology gaps or (in) making the breakthroughs in core technologies, Huawei...