Both are correct. The first sentence "I go live on Instagram every morning," is fine. The second sentence, "I do Instagram live every morning," sounds more informal and slightly colloquial or slang. It's sounds similar to when some people say "Let's do lunch/coffee" or "We did lunch/coffee." Or even "I do exercise every morning." Note that it should be "Instagram Live" with a capital "L" because this is the proper name for that service. So it would be more correct to write "I do Instagram Live every morning." 👍

The first is correct.

Just in terms of natural, casual speech both are fine. I suppose if you are writing or in a more formal setting "Every morning on Instagram I give a live presentation."