This is all true and it's referring to immigration generally. This is a specific type of immigration so let's talk about that specific type and not every other type.
This is immigration to staff augmentation body shops that are doing $150k/yr programming jobs with the company taking 25% off the top. It's not "immigrants starting businesses," it's not "the economy overall" it's targeting immigration suppressing the wages of a specific sector.
Maybe. I haven't seen that proven. I can easily imagine that making the US technology sector function more efficiently leads to higher employment. The fact that the US is home to all of the big tech companies is a boon to American employees, and this form of immigration is a boon to the big tech companies.